CBSE Class 5 Mathematics Revision Worksheet Set 28

Q1. Identify the following.
Answer: Based on the geometrical figures shown in the worksheet:
1. Figure 1 (with rays starting from point O passing through Q and P): An angle (specifically, \(\angle QOP\)).
2. Figure 2 (a line with an endpoint and an arrow): A ray.
3. Figure 3 (a closed polygon with 3 sides labeled 2 cm, 2.5 cm, and 3 cm, and vertices P, Q, R): A triangle (Scalene triangle).
4. Figure 4 (a triangle with a right-angle symbol at vertex M and vertices L, M, N): A right-angled triangle.
5. Figure 5 (an angle formed by two rays meeting at vertex Q with vertices P, Q, R): An obtuse angle / Triangle.
6. Figure 6 (two intersecting lines forming rays M and N): Intersecting lines / Straight line with rays.
In simple words: The figures represent basic geometrical shapes such as angles, rays, triangles, and intersecting lines.
Exam Tip: Memorize the basic definitions of geometric terms like rays, line segments, and various types of triangles and angles.

Q2. Find measure of 'X' in the following figure.

1. Triangle with angles \(55^\circ\), \(87^\circ\), and \(x\).
Answer:
Sum of angles in a triangle = \(180^\circ\)
\(55^\circ + 87^\circ + x = 180^\circ\)
\(142^\circ + x = 180^\circ\)
\(x = 180^\circ - 142^\circ\)
\(x = 38^\circ\)
In simple words: The sum of all three interior angles in any triangle is always \(180^\circ\). Subtract the given two angles from \(180^\circ\) to find the unknown angle.

Exam Tip: Always remember the angle sum property of a triangle: \(\text{Angle } 1 + \text{Angle } 2 + \text{Angle } 3 = 180^\circ\).

2. Right angle split into \(x\) and \(130^\circ\) (with a perpendicular indicator showing a \(90^\circ\) total or supplementary layout around a point). Looking at the figure, there is a right-angle symbol indicating \(90^\circ\) adjacent to \(130^\circ\), and angle \(x\). Let us use the linear pair / complete angle property where total angle on a straight line is \(180^\circ\) or around a point is \(360^\circ\). Based on the standard diagram showing a perpendicular line making \(90^\circ\) and total straight line: \(x + 90^\circ + 130^\circ\) or similar. Observing the standard layout: angles on a straight line sum to \(180^\circ\). Given the straight line with angles \(x\) and \(130^\circ\) (with a right-angle marker of \(90^\circ\)):
\(x + 90^\circ = 130^\circ\) or based on straight line \(180^\circ\). Let us calculate directly:
From the straight line, the angle \(x\) and \(130^\circ\) form a linear pair or complementary/supplementary relationship. Visually, the angle \(x\) and the right angle (\(90^\circ\)) combine with \(130^\circ\). Specifically, \(x + 90^\circ = 130^\circ \implies x = 40^\circ\), or using straight line \(180^\circ - 130^\circ = 50^\circ\). Let us state the standard step: Since the vertical line is perpendicular (\(90^\circ\)), \(x + (\text{angle}) = 90^\circ\). Here, \(130^\circ\) is an obtuse angle, so \(x = 180^\circ - 130^\circ = 50^\circ\) (linear pair with the adjacent angle if it forms a straight line).
Answer:
\(x = 180^\circ - 130^\circ = 50^\circ\) (if forming a linear pair on a straight line).
In simple words: Angles on a straight line always add up to \(180^\circ\).

Exam Tip: Identify straight lines in figures immediately to apply the linear pair rule (\(180^\circ\)).

3. An angle \(x\) and \(142^\circ\) forming a straight line.
Answer:
\(x + 142^\circ = 180^\circ\)
\(x = 180^\circ - 142^\circ\)
\(x = 38^\circ\)
In simple words: Two adjacent angles that form a straight line add up to \(180^\circ\).

Exam Tip: Supplementary angles on a straight line always sum to \(180^\circ\).

4. An angle \(x\) and \(82^\circ\) forming a right angle or straight line. Looking at the perpendicular symbol or straight line layout: Here, the total angle is a right angle (\(90^\circ\)) or a straight line (\(180^\circ\)). Assuming a right angle (\(90^\circ\)):
Answer:
\(x + 82^\circ = 90^\circ\)
\(x = 90^\circ - 82^\circ\)
\(x = 8^\circ\)
In simple words: Complementary angles add up to \(90^\circ\).

Exam Tip: Check for the small square symbol indicating a right angle (\(90^\circ\)).

5. Angles on a straight line with a right angle (\(90^\circ\)), \(x\), and \(35^\circ\).
Answer:
Sum of angles on a straight line = \(180^\circ\)
\(35^\circ + x + 90^\circ = 180^\circ\)
\(125^\circ + x = 180^\circ\)
\(x = 180^\circ - 125^\circ\)
\(x = 55^\circ\)
In simple words: All angles lying on a straight line add up to \(180^\circ\).

6. An angle \(135^\circ\) on a straight line.
Answer:
Let the missing angle on the straight line be \(x\):
\(x + 135^\circ = 180^\circ\)
\(x = 180^\circ - 135^\circ\)
\(x = 45^\circ\)
In simple words: A straight angle is \(180^\circ\). Subtract the given angle to find the remaining part.

Exam Tip: Linear pairs are supplementary (\(180^\circ\)).

Q3. If \(\angle DOB = 47^\circ\) find \(x\), \(y\) and \(\angle z\).
Answer:
Given intersecting lines AB and CD intersecting at O, with \(\angle DOB = 47^\circ\).
1. Finding \(z\):
\(\angle z\) and \(\angle DOB\) are vertically opposite angles.
\(z = \angle DOB = 47^\circ\)
2. Finding \(x\):
\(\angle x\) and \(\angle DOB\) form a linear pair on the straight line CD.
\(x + 47^\circ = 180^\circ\)
\(x = 180^\circ - 47^\circ = 133^\circ\)
3. Finding \(y\):
\(\angle y\) and \(\angle x\) are vertically opposite angles (or \(\angle y\) and \(\angle DOB\) are linear pair).
\(y = x = 133^\circ\) (or \(y = 180^\circ - 47^\circ = 133^\circ\))
In simple words: Vertically opposite angles are equal, and angles on a straight line add up to \(180^\circ\).

Exam Tip: Use vertical angles for quick equality and linear pairs for supplementary calculations (\(180^\circ\)).

Please refer to attached file for CBSE Class 5 Maths Revision Worksheets (4)