Question

EXERCISE 6.2
1. In Fig. 6.28, find the values of x and y and then
show that AB II CD.​

Answer 1

Step-by-step explanation:

$\blue{ \bf{ \underline{QUESTION} : }}$

1. In Fig. 6.28, find the values of x and y and then

show that AB II CD.

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$\boxed{ \huge{ \bold{Given}}}$

• $\angle \: A = 50 { \degree}$

• $\angle \: C= 130 { \degree}$

$\boxed{ \huge{ \bold{to \: find}}}$

• x and y value

• Prove that AB || CD

$\star{ \pink{ \underline{ \underline{Ｓｏｌｕｔｉｏｎ : - }}}}$

We Showed in Figure ➦

$\: \: \: \: \: \: \: \: \: \: {\implies{ \sf{ \angle \: A +{ \angle \: x = 180 \degree}}}}$

$\: \: \: \: \: \: \: \: \: \: {\implies{ \sf{ 50 \degree +{ \angle \: x = 180 \degree}}}}$

$\: \: \: \: \: \: \: \: \: \: {\implies{ \sf{ { \angle \: x = 180 \degree - 50 \degree}}}}$

$\: \: \: \: \: \: \: \: \: \: {\implies{ \sf{ { \angle \: x = {\boxed{ \red{130 \degree}}}}}}}$

$\: \: \: \: \: \: \: \: \: \: {\implies{ \sf{ \angle \: C+{ \angle \: y = 180 \degree}}}}$

$\: \: \: \: \: \: \: \: \: \: {\implies{ \sf{ 130 \degree +{ \angle \: y = 180 \degree}}}}$

$\: \: \: \: \: \: \: \: \: \: {\implies{ \sf{ { \angle \: y = 180 \degree - 130 \degree}}}}$

$\: \: \: \: \: \: \: \: \: \: {\implies{ \sf{ { \angle \: y = {\boxed{ \red{ 50 \degree }}}}}}}$

We Know that ➦

$\sf{ \angle \: x \: and \: {\angle \: y \: is \: a \: Vertically \: opposite \: angels}}$

So,

$\: \: \: \: \ \sf{x = y = 180 \degree}$

They are alternate interior Angles

AB II CD , Proved

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