Question

If two vertically opposite angles are supplementary, then the measure of one of the angles is _________.

• A. ${45}^{\circ }$
• B. ${90}^{\circ }$
• C. ${120}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

The correct option is B ${90}^{\circ }$



Vertically opposite angles are formed when two lines intersect.
Let us consider two lines XY and AB, such that they intersect at the point O.
Let ∠AOX = x
∠AOX = ∠BOY
[Vertically opposite angles are equal]
⇒ ∠AOX + ∠BOY = 180°
[Given: Vertically opposite angles are supplementary]
⇒ x + x = 180°
⇒ 2x = 180°
⇒ x = 90°
∴ The measure of one of the angles is 90°.