Question

In the figure given below, line, ab and CD intersect each other at O. find the value of x, y, z.

Answer 1

Hey user,

Z=84°(Vertical opposite angles)

2x + 84° = 180°(linear pair)
2x = 180°-84°
2x = 96
x = 96/2=48
x = 48
so, 2x = 96

75 + y = 96 (Vertical opposite angles)
y = 96-75
y = 21

Please mark it as the brainliest answer

Answer 2

$\huge\underline\mathfrak{Answer:}$

Since OC and OD are in the same line, therefore

$\angle$COA + $\angle$AOE + $\angle$EOD = 180°.

$\implies$ 84° + 75° + y = 180°.

$\implies$ 159° + y = 180°.

$\implies$ y = 180° - 159°

$\implies$ 21°.

Since AB and CD intersect at O, therefore

$\angle$BOD = $\angle$AOC

$\implies$ z = 84°.

Now, OC and OD are in the same line, therefore

$\angle$COB + $\angle$BOD = 180°

$\implies$ 2x + z = 180°.

$\implies$ 2x + 84° = 180°.

$\implies$ 2x = 96°.

$\implies$ x = 96° ÷ 2

$\implies$ 48°.

Hence, x = 48° , y = 21° and z = 84°.