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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 :

  1. 85°

  2. 105°

  3. 95°

  4. 175°

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 : Circles, Concise Mathematics Solutions ICSE Class 10.

Circles

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Answer

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°.

Hence, Option 1 is the correct option.

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