Question

Find the measure of arc DC, in degrees, where the ? is shown. D ? 49° 70° с B​

Answer 1

m(arc CD) = 122°

Explanation:

Since, measure of an arc = 2 × (Angle subtended by the arc at the circumference of the circle)

m(arc CD) = 2[m(∠CBD)]

By triangle sum theorem in ΔBCD,

m∠CBD + m∠BDC + m∠DCB = 180°

m∠CBD + 49° + 70° = 180°

m∠CBD = 180° - 119°

m∠CBD = 61°

Therefore, m(arc CD) = 2 × 61°

m(arc CD) = 122°