In the given triangle, CD is the bisector of ∠BCA. CD = DA. If ∠BDC = 76º, what is the degree measure of ∠CBD?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 66°.
CD = AD
So, ∠CAD = ∠ACD = y and ∠CDA = 104°
In triangle ACD, we have
⇒ ∠CAD + ∠ACD + ∠CDA = 180°
⇒ y + y + 104° = 180°
⇒ 2y = 76°
⇒ y = 38°
∠ BCD = ∠ ACD = 38°
Hence, in triangle BCD, we have
⇒ ∠BCD + ∠BDC + ∠CBD = 180°
⇒ 38° + 76° + ∠CBD = 180°
⇒ ∠CBD = 66°