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.`

Step-by-step 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 = (1)/(2)( m\angle BDC ) = (1)/(2) (126\degree) = 63 \degree`