Question

EXERCISE 11A
1. In the given figure, ABCD is a parallelogram in which
A = 70°. Calculate B, C and D.​

Answer 1

Answer:

if, A=70

then, C=70 (opp. angle of parallelogram)

A+B=180 (sum of adjacent angle of parallelogram)

70+B=180

B=180-70

B=110

B=D=110(opp. angle of parallelogram)

Answer 2

Correct Question :

In the given figure, ABCD is a parallelogram in which ∠A = 70°. Calculate ∠B, ∠C and ∠D.

Given :

• Measure of ∠A = 70°

To Find :

• The measures of ∠B , ∠C and ∠D

Solution :

In a parallelogram opposite angles are equal . From the figure ,

∠A = ∠C [ Opposite angles ]

∠B = ∠D [ Opposite angles]

Since , ∠A = 70°

$\\ \longrightarrow\pink{\sf{\angle A = \angle \: C= {70}^{ \circ} }}\:\bigstar$

Sum of the adjacent angles in a parallelogram is 180°. From the figure ,

∠A , ∠B and ∠C ,∠D are adjacent angles.

$\\ \longrightarrow \sf \angle \: A+ \angle \: B= {180}^{ \circ}$

$\\ \longrightarrow \sf \: {70}^{ \circ} + \angle \: B = {180}^{ \circ}$

$\\ \longrightarrow \sf \angle \: B = {180}^{ \circ} - {70}^{ \circ}$

$\\ \longrightarrow\pink{\sf{\angle \: B = {110}^{ \circ} }}\:\bigstar$

Since ∠B and ∠D are vertically opposite angles ,

$\\ \longrightarrow \sf \angle \: B = \angle \: D = {110}^{ \circ}$

Hence ,

• The measures of ∠B , ∠C and ∠D are 110° , 70° and 110°