Question

In the figure, given below, ∠ABC is equal to:

Options

• 105°

• 75°

• 90°

• 45°

Answer 1

105°

Explanation:

We know that,

Sum of co-interior angles in a trapezium is equal to 180°.

⇒ ∠A + ∠D = 180°

⇒ 105° + ∠D = 180°

⇒ ∠D = 180° − 105° = 75°

We know that,

The opposite angles of a cyclic quadrilateral is 180°.

In cyclic quadrilateral ABCD,

⇒ ∠D + ∠B = 180°

⇒ 75° + ∠B = 180°

⇒ ∠B = 180° − 75° = 105°