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In parallelogram ABCD, m∠A = 3x + 10 and m∠D = 2x + 30, Determine the m∠A.
a. 70°
b. 40°
c. 86°
d. 94°
d. Adjacent angles in a parallelogram are supplementary. ∠A and ∠D are adjacent angles. Thus, ∠A + ∠D = 180; 3x + 10 + 2x + 30 = 180. Simplifying, 5x + 40 = 180. Subtract 40 from end sides, 5x = 140. Divide both sides by 5; x = 28. ∠A = 3x + 10 or 3(28) + 10 which equals 94. If you select a, you considerd ∠A = ∠D. If you select b, you considered ∠A + ∠D = 90. If you select c, you solved for ∠D instead of ∠A.
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