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Quadrilateral ABCD is inscribed in this circle. What is the measure of ∠A ? Enter your answer in the box.
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Quadrilateral ABCD is inscribed in this circle.

What is the measure of ∠A ?

Enter your answer in the box.

Quadrilateral ABCD is inscribed in this circle. What is the measure of ∠A ? Enter-example-1
User Rohith Joseph
by
8.1k points

2 Answers

3 votes
One of the circle theorems is that opposite angles in a cyclic quadrilateral sum to 180°.
We can see that C is opposite to A, so in other words angle C + angle A = 180°. This can quickly be solved:
121+A=180
Minus 121 on both sides
A=59°
User Ophir Prusak
by
7.9k points
6 votes
arcDAB = 2*m∠C = 2*121 = 242°
arcDCB = 360° - arcDAB = 360 - 242 = 118°
m∠A = arcDCB/2 = 118/2 = 59°
User Matheno
by
7.3k points
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