Question

Quadrilateral ABCD ​ is inscribed in a circle.

What is the measure of angle A?


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m∠A=
°

Answer 1

`m\angle A=\boxed{135}\,^\circ`

Explanation:

Opposite angles of an inscribed quadrilateral are supplementary, so ...

m∠A + m∠C = 180°

Substituting the given expressions, we have ...

(3x +6)° + (x+2)° = 180°

4x +8 = 180 . . . . . . collect terms, divide by °

x +2 = 45 . . . . . . . . divide by 4

3x +6 = 135 . . . . . . multiply by 3

This is the value of angle A in degrees, so ...

m∠A = 135°