Question

Observe the given figure and find the value of unknown angles x and y.

• A. x = 72°, y = 22°
• B. x = 72°, y = 40°
• C. x = 112°, y = 40°
• D. x = 112°, y = 22°

Answer 1

The correct option is B x = 72°, y = 40°


Given:
∠AOE = 40°
∠DOB = 68°

For finding angle y:
∠AOE and ∠BOF are vertical angles.
So, ∠AOE = ∠BOF
∴ y = 40°

For finding angle x:
We know,
∠AOB = 180° (straight angle)

So,
$\angle AOE+\angle EOD+\angle DOB={180}^{\circ }$
$\Rightarrow {40}^{\circ }+\angle EOD+{68}^{\circ }={180}^{\circ }$
$\Rightarrow \angle EOD={180}^{\circ }-({40}^{\circ }+{68}^{\circ })$
$\Rightarrow \angle EOD={72}^{\circ }$

∠EOD and ∠COF are vertical angles.
So, ∠EOD = ∠COF
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∴ ∠COF = x = 72°

So, value of x = 72° and
value of y = 40°.