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The side AC of a \( \Large \triangle ABC \) is extended to D such that BC = CD. If \( \Large \angle ACB \) is \( \Large 70 ^{\circ} \), then what is \( \Large \angle ADB \) equal to?

A) \( \Large 35 ^{\circ} \)
B) \( \Large 45 ^{\circ} \)
C) \( \Large 70 ^{\circ} \)
D) \( \Large 110 ^{\circ} \)

Correct Answer:

A) \( \Large 35 ^{\circ} \)

Description for Correct answer:

\( \Large \angle ACB + \angle BCD = 180 ^{\circ} [linear\ pair] \)

\( \Large \angle BCD = 180 ^{\circ} - 70 ^{\circ} = 110 ^{\circ} \)

In \( \Large \triangle BCD, \)

\( \Large BC = CD \)

\( \Large \angle CBD = \angle CDB \) ...(i)

[angles opposite to equal sides]

Also, \( \Large \angle BCD + \angle CBD + \angle CDB = 180 ^{\circ} \)

\( \Large 2 \angle CDB = 180 ^{\circ} - \angle BCD \)

= \( \Large 180 ^{\circ} - 110 ^{\circ} = 70 ^{\circ} \)

\( \Large \therefore \angle CDB = \angle ADB \)

= \( \Large \frac{70 ^{\circ} }{2} = 35 ^{\circ} \)

Part of solved Geometry questions and answers : >> Elementary Mathematics >> Geometry

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