CBSE Class 5 Mathematics Revision Worksheet Set 20

Fill in the blanks:

Question (a). ____________ angles are a pair of angles that have a sum of \(180^\circ\).
Answer: Supplementary
In simple words: Two angles whose sum equals \(180^\circ\) are called supplementary angles.

Exam Tip: Remember 'S' for Supplementary and 'Straight' line (\(180^\circ\)) to avoid mixing it up with complementary (\(90^\circ\)).

Question (b). The angle that is the complement of half of a right angle is ____________.
Answer: \(45^\circ\) (or acute angle)
Half of a right angle = \(\frac{90^\circ}{2} = 45^\circ\)
Complement of \(45^\circ\) = \(90^\circ - 45^\circ = 45^\circ\)
In simple words: The complement of \(45^\circ\) is also \(45^\circ\) because they add up to \(90^\circ\).

Exam Tip: Always break down multi-step word problems into smaller parts: find half of the right angle first, then subtract from \(90^\circ\).

Question (c). An obtuse angle - Right angle = ____________ angle.
Answer: Acute
An obtuse angle is greater than \(90^\circ\) and less than \(180^\circ\). Subtracting \(90^\circ\) leaves a measure between \(0^\circ\) and \(90^\circ\), which is an acute angle.
In simple words: An angle less than \(90^\circ\) is an acute angle.

Exam Tip: Know the ranges: Acute (\(< 90^\circ\)), Right (\(90^\circ\)), Obtuse (\(90^\circ - 180^\circ\)), Straight (\(180^\circ\)).

Question (d). All linear pair are ____________ angles.
Answer: Supplementary
In simple words: Angles that form a linear pair always add up to \(180^\circ\), making them supplementary.

Exam Tip: Linear pairs are always adjacent and supplementary on a straight line.

Question (e). An alphabet with intersecting lines is ____________.
Answer: X (or T, V, Y, etc.)
In simple words: Letters like X have lines that cross each other at a point.

Question (f). The opposite sides of a rectangle are equal _________ and _________ to each other.
Answer: parallel, equal (or length, breadth)
In simple words: Opposite sides of a rectangle are both equal in length and parallel.

Exam Tip: Properties of a rectangle include equal opposite sides and parallel opposite sides.

Question (g). A ____________ is used to measure or construct angles.
Answer: protractor
In simple words: A protractor is the D-shaped tool used in geometry for angles.

Exam Tip: Spell geometrical instruments correctly in exams.

Question (h). A/An ____________ angle measures more than \(180^\circ\) but less than \(360^\circ\).
Answer: reflex
In simple words: An angle bigger than a straight line but smaller than a full circle is a reflex angle.

Exam Tip: Memorize the angle classifications by their degree limits.

Question (i). A ____________ angle measures exactly \(360^\circ\).
Answer: complete (or full turn)
In simple words: A full rotation around a point is \(360^\circ\).

Exam Tip: A complete angle represents one full circle.

Question (j). Complement of \(82^\circ\) is ____________.
Answer: \(8^\circ\)
\(90^\circ - 82^\circ = 8^\circ\)
In simple words: Subtract the given angle from \(90^\circ\) to find its complement.

Exam Tip: Complementary angles always sum up to \(90^\circ\).

Question (k). Supplement of \(180^\circ\) is ____________.
Answer: \(0^\circ\)
\(180^\circ - 180^\circ = 0^\circ\)
In simple words: Subtract \(180^\circ\) from \(180^\circ\) to get \(0^\circ\).

Exam Tip: Supplementary angles always sum up to \(180^\circ\).

Question (l). All ____________ angles share a common arm and a common vertex.
Answer: adjacent
In simple words: Adjacent angles sit side-by-side sharing a vertex and a side.

Exam Tip: Two conditions for adjacent angles: common vertex and common arm.

Question (m). Cross roads are an example of ____________ angles.
Answer: intersecting (or vertically opposite)
In simple words: Roads crossing each other form intersecting lines.

Exam Tip: Relate real-life models to geometrical concepts.

Question (n). Each angle of an Equilateral triangle measures ____________.
Answer: \(60^\circ\)
\(180^\circ \div 3 = 60^\circ\)
In simple words: All three angles of an equilateral triangle are equal, summing to \(180^\circ\).

Exam Tip: Equilateral triangles have both equal sides and equal \(60^\circ\) angles.

Question (o). A pair of ____________ lines extend endlessly and never meet at a point.
Answer: parallel
In simple words: Parallel lines always remain the same distance apart and never intersect.

Exam Tip: Railway tracks are a classic example of parallel lines.

Answer the following:

Q1. Is \(\Delta ABC\) with \(AB = 7\text{cm}\), \(BC = 10\text{cm}\), \(CA = 3\text{cm}\) possible? Give reasons for your answer.
Answer: No, it is not possible.
Reason: According to the triangle inequality property, the sum of the lengths of any two sides of a triangle must be strictly greater than the length of the third side.
Checking: \(AB + CA = 7 + 3 = 10\text{cm}\), which is equal to \(BC\) (\(10\text{cm}\)). Since \(10\) is not greater than \(10\), the triangle cannot be formed.
In simple words: The two shorter sides added together must be longer than the longest side.

Exam Tip: Always state the triangle inequality theorem clearly when testing if a triangle is possible.

Q2. An acute angle of a right triangle measures \(30^\circ\). Find the measure of other angles of the triangle.
Answer: The other two angles are \(90^\circ\) and \(60^\circ\).
Reason: Since it is a right-angled triangle, one angle is \(90^\circ\). The given acute angle is \(30^\circ\).
Using the angle sum property of a triangle (\(180^\circ\)):
Third angle = \(180^\circ - (90^\circ + 30^\circ)\)
\(= 180^\circ - 120^\circ = 60^\circ\)
In simple words: Subtract the known \(90^\circ\) and \(30^\circ\) from \(180^\circ\) to find the remaining angle.

Q3. Can a triangle have 2 obtuse angles? Give reasons.
Answer: No, a triangle cannot have 2 obtuse angles.
Reason: An obtuse angle is greater than \(90^\circ\). If a triangle had two obtuse angles, their sum alone would exceed \(180^\circ\) (\(> 90^\circ + 90^\circ = 180^\circ\)), which violates the angle sum property of a triangle that the sum of all three angles must be exactly \(180^\circ\).
In simple words: The total sum of all angles in a triangle is fixed at \(180^\circ\), so two angles cannot each be greater than \(90^\circ\).

Exam Tip: Remember that a triangle can have at most one obtuse or one right angle.

Q4. One right angle and one obtuse angle cannot form a linear pair? Give reasons.
Answer: True, they cannot form a linear pair.
Reason: A right angle measures \(90^\circ\) and an obtuse angle measures more than \(90^\circ\). Their sum will always be greater than \(90^\circ + 90^\circ = 180^\circ\). Since a linear pair must sum up to exactly \(180^\circ\), this combination is impossible.
In simple words: A linear pair must add up to exactly \(180^\circ\), but a right angle plus an obtuse angle always exceeds \(180^\circ\).

Exam Tip: Linear pairs always equal \(180^\circ\). Check if the sum equals \(180^\circ\) to test any pair of angles.

Q5. Can a triangle be drawn with its angles measuring \(66^\circ\), \(45^\circ\) and \(55^\circ\)? Why?
Answer: No, it cannot be drawn.
Reason: According to the angle sum property of a triangle, the sum of all three interior angles must be exactly \(180^\circ\).
Sum of given angles = \(66^\circ + 45^\circ + 55^\circ = 166^\circ\).
Since \(166^\circ \neq 180^\circ\), such a triangle is impossible.
In simple words: The three angles do not add up to \(180^\circ\), so the triangle cannot exist.

Exam Tip: Always add the given angles first when checking if a triangle is valid.

Q6. A straight angle is divided into 3 equal parts. What will be the measure of each part?
Answer: The measure of each part is \(60^\circ\).
Calculation:
Measure of a straight angle = \(180^\circ\)
Number of equal parts = 3
Measure of each part = \(\frac{180^\circ}{3} = 60^\circ\)
In simple words: Divide \(180^\circ\) by 3 to get equal shares.

Exam Tip: Straight angle = \(180^\circ\); complete angle = \(360^\circ\); right angle = \(90^\circ\).

Q7. Which of the following forms a supplementary pair of angles? (Give Reasons)
(a) \(74^\circ\) and \(58^\circ\)
(b) \(93^\circ\) and \(87^\circ\)
Answer: (b) \(93^\circ\) and \(87^\circ\) form a supplementary pair.
Reasons:
For (a): \(74^\circ + 58^\circ = 132^\circ\) (Not supplementary, as sum is not \(180^\circ\)).
For (b): \(93^\circ + 87^\circ = 180^\circ\) (Supplementary, because their sum is exactly \(180^\circ\)).
In simple words: Supplementary angles must add up to \(180^\circ\). Only option (b) does this.

Exam Tip: Always test pairs by adding them together to check if they reach \(180^\circ\).

Q8. Which of the following forms a complementary pair of angles? (Give Reasons)
(a) \(50^\circ\) and \(55^\circ\)
(b) \(68^\circ\) and \(22^\circ\)
Answer: (b) \(68^\circ\) and \(22^\circ\) form a complementary pair.
Reasons:
For (a): \(50^\circ + 55^\circ = 105^\circ\) (Not complementary, as sum is not \(90^\circ\)).
For (b): \(68^\circ + 22^\circ = 90^\circ\) (Complementary, because their sum is exactly \(90^\circ\)).
In simple words: Complementary angles must add up to \(90^\circ\). Only option (b) satisfies this.

Exam Tip: Remember: Complementary = \(90^\circ\); Supplementary = \(180^\circ\).

Q9. All Supplementary angles are not linear pair of angles. (Give reasons)
Answer: This statement is true.
Reason: Two angles can be supplementary (their sum is \(180^\circ\)) without being adjacent or lying on the same straight line (for example, two separate angles measuring \(110^\circ\) and \(70^\circ\) anywhere on paper). A linear pair specifically requires the supplementary angles to be adjacent and form a straight line.
In simple words: Supplementary just means adding to \(180^\circ\), but a linear pair also requires the angles to be right next to each other on a straight line.

Exam Tip: All linear pairs are supplementary, but not all supplementary angles form a linear pair.

Q10. In a right-angled triangle, if one angle measures \(35^\circ\), find each of the remaining two angles.
Answer: The remaining two angles are \(90^\circ\) and \(55^\circ\).
Reason:
1. Since it is a right-angled triangle, one angle is always \(90^\circ\).
2. The third angle is found using the angle sum property:
Third angle = \(180^\circ - (90^\circ + 35^\circ)\)
\(= 180^\circ - 125^\circ = 55^\circ\)
In simple words: One angle is \(90^\circ\) by definition, and the other acute angle is \(90^\circ - 35^\circ = 55^\circ\).

Question (a). A \(109^\circ\) angle is a/an ____________ angle.
(i) acute
(ii) right
(iii) obtuse
(iv) reflex
Answer: (iii) obtuse
An angle measuring between \(90^\circ\) and \(180^\circ\) is an obtuse angle.
In simple words: \(109^\circ\) is greater than \(90^\circ\) but less than \(180^\circ\), so it is obtuse.

Exam Tip: Check if the angle is larger than \(90^\circ\) and smaller than \(180^\circ\).

Question (b). A \(198^\circ\) angle is a/an ____________ angle.
(i) acute
(ii) straight
(iii) reflex
(iv) obtuse
Answer: (iii) reflex
An angle measuring more than \(180^\circ\) and less than \(360^\circ\) is a reflex angle.
In simple words: Since \(198^\circ\) is greater than \(180^\circ\), it is a reflex angle.

Exam Tip: Reflex angles always exceed a straight line (\(180^\circ\)).

Question (c). Each of the following is smaller than a straight angle, except ____________ angle.
(i) acute
(ii) obtuse
(iii) reflex
(iv) right
Answer: (iii) reflex
A straight angle measures \(180^\circ\). Acute (\(<90^\circ\)), right (\(90^\circ\)), and obtuse (\(90^\circ - 180^\circ\)) are all smaller than \(180^\circ\), whereas a reflex angle (\(>180^\circ\)) is larger.
In simple words: Reflex angles are larger than straight angles, while all others are smaller.

Exam Tip: Compare the size of each angle type with \(180^\circ\).

Question (d). The rays forming \(\angle ABC\) are
(i) \(\overrightarrow{AB}\) and \(\overrightarrow{BC}\)
(ii) \(\overrightarrow{AB}\) and \(\overrightarrow{CB}\)
(iii) \(\overrightarrow{BA}\) and \(\overrightarrow{BC}\)
(iv) \(\overrightarrow{BA}\) and \(\overrightarrow{CB}\)
Answer: (iii) \(\overrightarrow{BA}\) and \(\overrightarrow{BC}\)
The vertex of the angle is \(B\). The rays starting from vertex \(B\) going towards \(A\) and \(C\) are denoted as \(\overrightarrow{BA}\) and \(\overrightarrow{BC}\).
In simple words: The rays forming an angle always start from the middle letter (vertex).

Exam Tip: The middle letter in an angle notation like \(\angle ABC\) is always the vertex.

Question (e). The complement of an angle of \(65^\circ\) is
(i) \(15^\circ\)
(ii) \(25^\circ\)
(iii) \(30^\circ\)
(iv) \(35^\circ\)
Answer: (ii) \(25^\circ\)
Complement = \(90^\circ - 65^\circ = 25^\circ\)
In simple words: Subtract \(65^\circ\) from \(90^\circ\) to find the complement.

Exam Tip: Complementary angles add up to \(90^\circ\).

Question (f). If 2 equal angles are complementary, the measure of each angle would be:
(i) \(30^\circ\)
(ii) \(45^\circ\)
(iii) \(60^\circ\)
(iv) \(90^\circ\)
Answer: (ii) \(45^\circ\)
Since the angles are equal and complementary, their sum is \(90^\circ\).
Each angle = \(\frac{90^\circ}{2} = 45^\circ\)
In simple words: Divide \(90^\circ\) equally into two parts.

Exam Tip: Equal complements are always \(45^\circ\) each (\(45^\circ + 45^\circ = 90^\circ\)).

Question (g). The sum of 3 angles of a triangle are:
(i) \(90^\circ\)
(ii) \(100^\circ\)
(iii) \(120^\circ\)
(iv) \(180^\circ\)
Answer: (iv) \(180^\circ\)
The angle sum property states that the sum of interior angles of any triangle is \(180^\circ\).
In simple words: The three angles of any triangle always add up to \(180^\circ\).

Question (h). A triangle having all sides of different length is called ____________ triangle.
(i) equilateral
(ii) right
(iii) scalene
(iv) isosceles
Answer: (iii) scalene
A triangle with all unequal sides is a scalene triangle.
In simple words: Different side lengths mean a scalene triangle.

Exam Tip: Equilateral = all equal sides; Isosceles = two equal sides; Scalene = all different sides.

Question (i). Two angles of a triangle are \(40^\circ\) and \(25^\circ\). Third angle would be
(i) \(35^\circ\)
(ii) \(65^\circ\)
(iii) \(25^\circ\)
(iv) \(115^\circ\)
Answer: (iv) \(115^\circ\)
Third angle = \(180^\circ - (40^\circ + 25^\circ)\)
\(= 180^\circ - 65^\circ = 115^\circ\)
In simple words: Add the two given angles and subtract from \(180^\circ\).

Exam Tip: Double-check your addition and subtraction steps.

Question (j). In an equilateral triangle
(i) all sides are equal
(ii) all angles are equal
(iii) both (i) and (ii)
(iv) none of these
Answer: (iii) both (i) and (ii)
An equilateral triangle has all three sides equal and all three angles equal (\(60^\circ\) each).
In simple words: Equilateral triangles have equal sides and equal angles.

Exam Tip: 'Equilateral' means equal sides and equal angles go hand in hand.