CBSE Class 7 Mathematics Lines And Angles Worksheet Set 01

Question. In the given Fig. i.e., ∠1 50 then find ∠2, ∠3, ∠4.

Answer : ∠2 = 130°, ∠3 = 50°, ∠4 = 130°

Question. Two angles of a linear pair are in the ratio 2 : 7, find the angles.
Answer : 40°, 140°

Question. Find the angle which is (1/5)th of its complementry angle.
Answer : 15°

Question. The difference in the measure of two supplementry angles is 80°, find the measures of the angles.
Answer : 50°, 130°

Question. Find complement of the following angles : m
(a) 20°
(b) 66°
(c) 40°
(d) 35°
Answer : (a) 70° (b) = 24° (c) 50° (d) = 55°

Question. Find the angle which is equal to its complement.
Answer : 45°

Question. An angle is greater than 80° than its supplement. What is its supplementary angle
Answer : 130°

Question. Two complementary angle are in the ratio 2 : 3, find the angles.
Answer : 36°, 54°

Question. Two supplementry angles are in the ratio 2 : 3, find the smallest angle.
Answer : 72°

Question. An angle is equal to 5 times its complement. Determine its measure.
Answer : 15°, 75°

Question. Find the angle which is equal to its supplement.
Answer : 90°

Question. An angle is 20° greater than its complementry angle. What is the complementry angle.
Answer : 35°

Question. An angle is equal to 8 times its supplement. Determine its measure.
Answer : 20°, 160°

Question. Find the angle which is one third of its supplementry angle.
Answer : 45°

Question. An angle is equal to double of its complement. Determine its measure
Answer : 60°

Question. Find supplement of the following angles.
(a) 105°
(b) 87°
(c) 154°
Answer : a = 75°; b = 93°; c = 26°

Question. An angle is greater than 30° than its complement. What the measurement of complementary angles?
Answer : 60°, 30°

Question. Two complementry angles are in the ratio 4 : 5, find the greater angle.
Answer : 50°

Question. An angle is greater than 60° than its supplementary angle. What is the supplementary angle?
Answer : 60°

Question. The difference of the measures of two complementry angles is 40°. Find the measures of the angles
Answer : 25°, 65°.

Question. Find the angle which is 9 times of its supplementry angle.
Answer : 162°

Question. Two supplementary angles are in the ratio 3 : 7, find the angles.
Answer : 54°, 126°

Question. Two angles of a linear pairs are in the ratio 1 : 5 find angles.
Answer : 30°, 150°

Question. Find the angle which is half of its complementary angle.
Answer : 30°

Question. Identify which of the following pair of angles are complementary and which are supplementary :
(a) 63°, 117°
(b) 23°, 67°
(c) 105°, 75°
(d) 120°, 60°.
Answer : Complementry = b, Supplementry = a, c, d

Question. An angle is greater then 25° than its complement. What is its complementary angle?
Answer : 57.5°

Question. An angle is equal to 3 times of its supplement. Determine its measure.
Answer : 135°

Question 1. In the adjoining figure:
(i) Is ∠1 adjacent to ∠2?
(ii) Is ∠AOC adjacent to ∠AOE?
(iii) Do ∠COE and ∠EOD form a linear pair?
(iv) Are ∠BOD and ∠DOA supplementary?
(v) Is ∠1 vertically opposite to ∠4?
(vi) What is the vertically opposite angle of ∠5?
Answer:
(i) **Yes.** They sit right next to each other. They share the center point \(O\) and the middle line \(OC\).
(ii) **No.** Even though they share the center point \(O\) and the line \(OA\), they overlap. One angle is inside the other.
(iii) **Yes.** These two angles lie on the straight line \(CD\). Together, they form a flat straight angle.
(iv) **Yes.** They lie on the straight line \(AB\). Their measures add up to \(180^\circ\).
(v) **Yes.** They are directly across from each other where the two lines cross.
(vi) The vertically opposite angle of \(\angle 5\) is \(\angle COB\) (which can also be written as \(\angle 2 + \angle 3\)).

In simple words: Angles are adjacent when they sit side-by-side without overlapping. Angles that make a straight line are supplementary and form a linear pair.

Exam Tip: To find if angles are adjacent, check if they share a corner, a middle line, and do not share any inside space.

Question 2. Indicate which pairs of angles in question 1 are:
(i) Vertically opposite angles.
(ii) Linear pairs.
Answer:
(i) Vertically opposite angles:
- \(\angle 1\) and \(\angle 4\) (which are \(\angle AOC\) and \(\angle BOD\))
- \(\angle 5\) and \(\angle BOC\) (where \(\angle BOC\) is the combined angle \(\angle 2 + \angle 3\))

(ii) Linear pairs:
- \(\angle 1\) and \(\angle 5\) (they form the straight line \(CD\))
- \(\angle 5\) and \(\angle 4\) (they form the straight line \(AB\))
- \(\angle 4\) and \(\angle BOC\) (where \(\angle BOC\) is \(\angle 2 + \angle 3\); they form the straight line \(CD\))
- \(\angle 1\) and \(\angle BOC\) (where \(\angle BOC\) is \(\angle 2 + \angle 3\); they form the straight line \(AB\))
In simple words: Vertically opposite angles are directly across from each other. Linear pairs are side-by-side angles that make a flat straight line.

Exam Tip: Remember that the non-shared sides of a linear pair must always point in opposite directions to form a straight line.

Question 3. Fill in the blanks:
(i) If two angles are complementary, then the sum of their measures is _______.
(ii) If two angles are supplementary, then the sum of their measures is ______.
(iii) Two angles forming a linear pair are _______________.
(iv) If two adjacent angles are supplementary, they form a ___________.
(v) If two lines intersect at a point, then the vertically opposite angles are always_____________.
(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are __________.
Answer:
(i) **\( 90^\circ \)** - Complementary angles always add up to a right angle.
(ii) **\( 180^\circ \)** - Supplementary angles always add up to a straight line.
(iii) **supplementary** - A linear pair of angles lies on a straight line, so their sum is \( 180^\circ \).
(iv) **linear pair** - Adjacent angles that add up to \( 180^\circ \) form a straight line together.
(v) **equal** - When two lines cross, the opposite angles are always identical in size.
(vi) **obtuse angles** - If one set of opposite angles is small (less than \( 90^\circ \)), the other set must be large (more than \( 90^\circ \)) to complete the circle.
In simple words: Complementary angles make a corner right-angle. Supplementary angles and linear pairs make a flat straight line.

Exam Tip: Memorize these basic terms as they are very common in matching and fill-in-the-blank exam questions.