Question

The figure shows ∆ABC inscribed in circle D. If m ∠CBD = 32°, find m ∠BAC, in degrees.

Answer 1

ANSWER

$m\angle BAC =63 \degree.$

EXPLANATION

From isosceles triangle CBD,

$m \angle \: CBD = m\angle BCD=32\degree$

This implies that,

$m\angle BDC + 32 \degree + 32 \degree = 180 \degree$

$m\angle BDC + 64\degree = 180 \degree$

$m\angle BDC = 180 \degree - 64\degree$

$m\angle BDC = 126\degree$

$m\angle BAC = \frac{1}{2}( m\angle BDC ) = \frac{1}{2} (126\degree) = 63 \degree$