Question

In the figure,find the four angles A,B,C,D of the parallelogram ABCD​

Answer 1

★ Provided Question ★

In the figure,find the four angles A,B,C,D of the parallelogram ABCD.

★ Required Solution ★

Here, $\rm { \triangle ABC }$ is forming in the $\rm { ||gram ABCD }$.

In the $\rm { \triangle ABC }$ ,we have:–

• Measurement of the three angle = $\rm { 5x° ,7x° \: and \: 6x° }$

We know that sum of the interior angles of the triangle are 180°.So,

$\rm { \longrightarrow 5x° + 7x° + 6x° = 180° }$

$\rm { \longrightarrow 18x° = 180° }$

$\rm { \longrightarrow x° =\cancel{ \dfrac{ 180° }{18} }}$

$\rm { \longrightarrow x° = 10° }$

So the angles of the triangle are:–

• $\rm { 5x° = (5 \times 10)° = 50°}$
• $\rm { 7x° = (7 \times 10)° = 70°}$
• $\rm { 6x° = (6 \times 10)° = 60°}$

And,

• $\rm { \angle CAB = \angle ACD }$ [ By alternate interior property ]

$\rm { \implies 5x° = \angle ACD }$

$\rm { \implies 50° = \angle ACD }$

Therefore,

$\rm { \implies \angle C = \angle ACB + \angle ACD}$

$\rm { \implies \angle C = 50° + 60° }$

$\rm { \implies \angle C = 110° }$

$\boxed { \large \bf \red { \angle C = 110° } }$

Also,

• $\rm { \angle C = \angle A }$ [ As the opposite angles of a parallelogram are equal ]

$\rm { \implies \angle A = 110° }$

$\boxed { \large \bf \red { \angle A = 110° } }$

___

$\boxed { \large \bf \red { \angle B = 70° } }$

[ Found in the triangle ABC]

• $\rm { \angle D = \angle B }$ [ As the opposite angles of a parallelogram are equal ]

$\rm { \implies \angle D = 70° }$

$\boxed { \large \bf \red { \angle D = 70° } }$

So, done!!

_______________________________