Question

Quadrilateral upper M upper A upper T upper H is drawn within a circle such that all vertices touch the edge of the circle. The arc joining upper A and upper T is labeled 50 degrees. The arc joining upper T and upper H is marked 170 degrees.
The image shows an inscribed quadrilateral. The mAM=54°
. Determine the m∠A
.

(1 point)
m∠A=

°

Answer 1

m(arc AM) = 54°, m(arc AT) = 50°, m(arc TH) = 170°.
So m(arc MH) = 360 − (54 + 50 + 170) = 86°.
Arc MT (opposite ∠A) = arc MH + arc HT = 86 + 170 = 256°.
Thus m∠A = 1/2 · 256° = 128°.

m∠A = 128°.