in a cyclic quadrilateral ABCD, twice the measure of angle A is thrice the measure of angle C, find the measure...
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Twice the measure of angle A is thrice the measure of angle C:
⇒ 2A = 3C
⇒ A : C = 3 : 2
Define x:
Let x be the constant ratio
A : C = 3x : 2x
Cyclic quadrilateral is a quadrilateral inscribed in a circle.
⇒ The sum of the opposite angles of a cyclic quadrilateral is supplementary.
Solve x:
3x + 2x = 180
5x = 180
x = 36º
Find Angle C:
Angle C = 2x = 2(36) = 72º
Answer: Angle C is 72º
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