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=
°
To solve for the measure of angle A, we can use the property that the sum of the angles in a quadrilateral is 360 degrees.
m∠A + m∠M + m∠T + m∠H = 360
Given that m∠M = 54 degrees, and we know the measures of arcs AT and TH in the circle, we can find m∠T and m∠H.
m∠T = 50 degrees (from the arc joining A and T)
m∠H = 170 degrees (from the arc joining T and H)
Now we can substitute these values into the equation:
m∠A + 54 + 50 + 170 = 360
m∠A + 274 = 360
m∠A = 360 - 274
m∠A = 86 degrees
Therefore, the measure of angle A is 86 degrees.