2. Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.
1 answer:
Ans: 1. m ∠C = 88° 2. m ∠B = 100° 3. m ∠A = 92° 4. m ∠D = 80° Explanation: ∠A and ∠C are supplementary angles; therefore: ∠A + ∠C = 180° --- (A) Since, ∠A = (x+2)° and ∠C = (x-2)° Plug-in the values in equation (A): (A) => (x+2)° + (x-2)° = 180° => x° + 2° + x° - 2° = 180° => 2x° = 180° => x = 90° Since x = 90°, therefore,∠A = (x+2)° = 92°, and∠C = (x-2)° = 88° Since ∠B and ∠D are supplementary angles; therefore, ∠B + ∠D = 180° ∠B + (x-10)° = 180° Since, x = 90°; therefore, ∠B + 80° = 180°∠B = 100° And since, ∠B + ∠D = 180° and ∠B = 100° Therefore, ∠D = 180° - 100°∠D= 80° -i
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