Answer:
Measure of arc CD = 112°
Explanation:
Since quadrilateral ABCD is a cyclic quadrilateral,
m∠A + m∠C = 180°
129° + m∠C = 180°
m∠C = 180° - 129°
m∠C = 51°
Since, m(arc BD) = 2(m∠C) [Since measure of the arc is double of its inscribed angle]
= 2(51°)
= 102°
Since, m(arc BD) + m(arc CD) + m(arc BC) = 360°
102° + m(arc CD) + 146° = 360°
m(arc CD) = 360° - (102° + 146°)
= 112°
Therefore, measure of arc CD is 112°.