InterviewSolution
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InterviewSolution
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In □ABCD, side BC || side AD, side AB ≅ side DC. If ∠A = 72°, then find the measures of ∠B and ∠D. Construction: Draw seg BP ⊥ side AD, A – P – D, seg CQ ⊥ side AD, A – Q – D. |
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Answer» i. ∠A = 72° [Given] In □ABCD, side BC || side AD and side AB is their transversal. [Given] ∴ ∠A + ∠B = 180° [Interior angles] ∴ 72° +∠B = 180° ∴ ∠B = 180° – 72° = 108° ii. In ∆BPA and ∆CQD, ∠BPA ≅ ∠CQD [Each angle is of measure 90°] Hypotenuse AB ≅ Hypotenuse DC [Given] seg BP ≅ seg CQ [Perpendicular distance between two parallel lines] ∴ ∆BPA ≅ ∆CQD [Hypotenuse side test] ∴ ∠BAP ≅ ∠CDQ [c. a. c. t.] ∴ ∠A = ∠D ∴ ∠D = 72° ∴ ∠B = 108°, ∠D = 72° |
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