The value of x is 10 and y is 20.
Solution:
Sum of the adjacent angles in a straight line = 180
⇒ 7x° + 90° + 20° = 180°
⇒ 7x° + 110° = 180°
Subtract 110° from both sides.
⇒ 7x° = 70°
Divide by 7 on both sides.
⇒ x° = 10°
In the image, 90° and (5x° + 2y°) are vertically opposite anlges.
If two lines are intersecting, then vertically opposite angles are equal.
⇒ (5x° + 2y°) = 90°
⇒ 5(10°) + 2y° = 90°
⇒ 50° + 2y° = 90°
Subtract 50° from both sides.
⇒ 2y° = 40°
Divide by 2 on both sides.
⇒ y° = 20°
Hence the value of x is 10 and y is 20.