Question

F ∠A is 95° and ∠B is 105°, what is ∠C?
A) 75°
B) 85°
C) 95°
D) 105°

Answer 1

A)75

Explanation:

Opposite angles in an inscribed quadrilateral are supplementary.

∠B + ∠D = 180°

105° + ∠D = 180°

∠D = 75°

Answer 2

The question is missing important data. The quadrilateral having vertices A, B, C and D is a cyclic quadrilateral.

Answer:

B) 85°

Explanation:

Given:

A cyclic quadrilateral with ∠A is 95° and ∠B is 105°.

For a cyclic quadrilateral, the sum of the opposite interior angles is equal to 180°

Therefore, sum of angles A and C is 180°.

`\angle A + \angle C=180\°\\95\°+\angle C=180\°\\\angle C=180-95\\\angle C =85\°`

Therefore, the correct option is option B) 85°