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

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

ribed in a circle. The vertices of quadrilateral lie on the edge of the circle and are labeled as A, B, C, D. The interior angle C is labeled as 121 degrees.

Mathematics

1 answer:

Lubov Fominskaja [6] · Answer 1 · 2022-03-23T18:41:16+03:00

Answer: The measure of angle A is 59 degrees.

When you have a quadrilateral inscribed in a circle the opposite sides are always supplementary (add to 180). Given the order of the vertices of our quadrilateral, we know that A and C are opposite.

Therefore, we can write and solve the following equation.
A + C = 180
A + 121 = 180
A = 59 degrees