Seudónimo Seudónimo

07-03-2018
Mathematics

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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 your answer in the box class=

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Banabanana Banabanana

07-03-2018

arcDAB = 2*m∠C = 2*121 = 242°
arcDCB = 360° - arcDAB = 360 - 242 = 118°
m∠A = arcDCB/2 = 118/2 = 59°

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carlafossil320 carlafossil320

07-03-2018

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°

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