Question

∆ABC is inscribed inside a circle and there is a point D on the arc BC opposite to A such that BD = CD. If ∠BAC = 70° and ∠ABD = 85°, then find the measure of ∠BCA.

• A. 45
• B. 50
• C. 55
• D. 60

Answer 1

Answer:

D. 60

 

opposite angles in a cyclic quadrilateral are supplementary.

∠BAC + ∠BDC = 180°

∠ABD + ∠ACD = 180°

∠BDC = 110°

∠ACD = 95°

In ∆BCD:

∠BCD = ∠CBD [BD = CD]

∠BCD + ∠CBD + ∠BDC = 180°

∠BCD = 35°

∠ACD = 95°

∠BCA + ∠BCD = 95°

∠BCA = 60°