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

45^{\circ}

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90^{\circ}

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120^{\circ}

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100^{\circ}

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Solution

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°.

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Similar questions

Fill in the blanks:

(i) If two angles are complementary, then the sum of their measures is _______.

(ii) If two angles are supplementary, then the sum of their measures is _______.

(iii) Two angles forming a linear pair are _______.

(iv) If two adjacent angles are supplementary, they form a _______.

(v) If two lines intersect at a point, then the vertically opposite angles are always _______.

(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are _______.

Q. Angles which are both supplementary and vertically opposite are:

The sum of an angle and one third of its supplementary angle is $90^{\circ}$ . The measure of the angle is
(a) $135^{\circ}$
(b) $120^{\circ}$
(c) $60^{\circ}$
(d) $45^{\circ}$

Q. Two angles are supplementary angles. If measure of one angle is

66^{\circ}

, then find the measure of another angle.

Question 5
Angles, which are both suplementary and vertically opposite are
(a) $95^{\circ}, 85^{\circ}$
(b) $90^{\circ}, 90^{\circ}$
(c) $100^{\circ}, 80^{\circ}$
(d) $45^{\circ}, 45^{\circ}$

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