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Given angle DEF = (4x + 27) degrees and arc FGD = (16x - 21) degrees, find x and angle DEF.

 

 Mar 2, 2021
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When a quadrilateral is inscribed in a circle, the sum of the opposite angles is 180 degrees.

 

∠DEF + ∠FGD = 180

 

4x + 27 + 16x - 21 = 180

 

x = 8.7

 

∠DEF = 4x + 27 = 4*8.7 + 27 = 61.8º

 

∠FGD = 16x - 21 = 16*8.7 - 21 = 118.2º

 Mar 3, 2021

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