Question

ABCD is a trapezium with AD parallel to BC. Side BC is produced to point E and angle DCE = 95°. Angle B is equal to:

Options

• 85°

• 105°

• 95°

• 175°

Answer 1

85°

Explanation:

Given,

AD || BC

Since,

Side BC is produced to point E.

We can say that,

AD || BE

From figure,

∠ADC = ∠DCE = 95° (Alternate angles are equal)

We know that,

The opposite angles of a cyclic quadrilateral are supplementary.

∴ ∠ADC + ∠CBA = 180°

⇒ ∠CBA = 180° − ∠ADC

= 180° − 95°

= 85°