NCERT Exemplar Solutions
Class 7 - Mathematics - Unit 5: Lines And Angles

Problems and Solutions

72. Write down each pair of adjacent angles shown in the following figures:

73. In each of the following figures, write, if any, (i) each pair of vertically opposite angles, and (ii) each linear pair.

74. Name the pairs of supplementary angles in the following figures:

75. In Fig. 5.36, PQ ∥ RS, TR ∥ QU and ∠PTR = 42°. Find ∠QUR.

76. The drawings below (Fig. 5.37) show angles formed by the goalposts at different positions of a football player. The greater the angle, the better the chance the player has of scoring a goal.

(a) Seven football players are practicing their kicks. They are lined up in a straight line in front of the goalpost [Fig. (ii)]. Which player has the greatest kicking angle?

(b) Now the players are lined up as shown in Fig. (iii). Which player has the best kicking angle?

(c) Estimate at least two situations such that the angles formed by different positions of two players are complement to each other.

The sum of two vertically opposite angles is 166°. Find each of the angles.

78. In Fig. 5.38, l ∥ m ∥ n. ∠QPS = 35° and ∠QRT = 55°. Find ∠PQR.

79. In Fig. 5.39, P, Q and R are collinear points and TQ ⟂ PR. Name:

(a) pair of complementary angles

(b) two pairs of supplementary angles

(c) four pairs of adjacent angles

80. In Fig. 5.40, OR ⟂ OP.

(i) Name all the pairs of adjacent angles.

(ii) Name all the pairs of complementary angles.

81. If two angles have a common vertex and their arms form opposite rays (Fig. 5.41), then:

(a) How many angles are formed?

(b) How many types of angles are formed?

(c) Write all the pairs of vertically opposite angles.

82. In Fig. 5.42 are the following pairs of angles adjacent? Justify your answer.

83. In Fig. 5.43, write all the pairs of supplementary angles.

84. What is the type of other angle of a linear pair if

(a) one of its angles is acute?

(b) one of its angles is obtuse?

(c) one of its angles is right?

Can two acute angles form a pair of supplementary angles? Give reason in support of your answer.

86. Two lines AB and CD intersect at O (Fig. 5.44). Write all the pairs of adjacent angles by taking angles 1, 2, 3 and 4 only.

If the complement of an angle is 62°, then find its supplement.

88. A road crosses a railway line at an angle of 30° as shown in Fig. 5.45. Find the values of a, b and c.

89. The legs of a stool make an angle of 35° with the floor as shown in Fig. 5.46. Find the angles x and y.

90. Iron rods a, b, c, d, e and f are making a design in a bridge as shown in Fig. 5.47, in which a ∥ b, c ∥ d, e ∥ f. Find the marked angles between

(i) b and c

(ii) d and e

(iii) d and f

(iv) c and f

91. Amisha makes a star with the help of line segments a, b, c, d, e and f, in which a ∥ d, b ∥ e and c ∥ f. Chhaya marks an angle as 120° as shown in Fig. 5.48 and asks Amisha to find the ∠x, ∠y and ∠z. Help Amisha in finding the angles.

92. In Fig. 5.49, AB ∥ CD, AF ∥ ED, ∠AFC = 68° and ∠FED = 42°. Find ∠EFD.

93. In Fig. 5.50, OB is perpendicular to OA and ∠BOC = 49°. Find ∠AOD.

94. Three lines AB, CD and EF intersect each other at O. If ∠AOE = 30° and ∠DOB = 40° (Fig. 5.51), find ∠COF.

Measures (in degrees) of two complementary angles are two consecutive even integers. Find the angles.

If a transversal intersects two parallel lines, and the difference of two interior angles on the same side of a transversal is 20°, find the angles.

Two angles are making a linear pair. If one of them is one-third of the other, find the angles.

Measures (in degrees) of two supplementary angles are consecutive odd integers. Find the angles.

99. In Fig. 5.52, AE ∥ GF ∥ BD, AB ∥ CG ∥ DF and ∠CHE = 120°. Find ∠ABC and ∠CDE.

100. In Fig. 5.53, find the value of ∠BOC, if points A, O and B are collinear.

101. In Fig. 5.54, if l ∥ m, find the values of a and b.

102. In Fig. 5.55, l ∥ m and a line t intersects these lines at P and Q, respectively. Find the sum 2a + b.

103. In Fig. 5.56, QP ∥ RS. Find the values of a and b.

104. In Fig. 5.57, PQ ∥ RT. Find the value of a + b.

105. In Fig. 5.58, PQ, RS and UT are parallel lines.

(i) If c = 57° and a = c/3, find the value of d.

(ii) If c = 75° and a = (2/5)c, find b.

106. In Fig. 5.59, AB ∥ CD. Find the reflex ∠EFG.

107. In Fig. 5.60, two parallel lines l and m are cut by two transversals n and p. Find the values of x and y.

108. In Fig. 5.61, l, m and n are parallel lines, and the lines p and q are also parallel. Find the values of a, b and c.

109. In Fig. 5.62, state which pair of lines are parallel. Give reason.

110. In Fig. 5.63, examine whether the following pairs of lines are parallel or not:

(i) EF and GH

(ii) AB and CD

111. In Fig. 5.64, find out which pair of lines are parallel:

112. In Fig. 5.65, show that:

(i) AB ∥ CD

(ii) EF ∥ GH

113. In Fig. 5.66, two parallel lines l and m are cut by two transversals p and q. Determine the values of x and y.