Question

Inquadrilateral ABCD side BC is parallel to side AD, side AB is congruent to side CD. If angle A=72⁰. Then find the measure of angle B and angle D.
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Answer 1

Answer:

Draw seg BP ⊥ side AD, A – P – D, seg CQ ⊥ side AD, A – Q – D. 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°

Answer 2

Answer:

i. ∠A = 72° [Given] In ABCD, side BC || side AD and side AB is their transversal. [Given]

Step-by-step explanation:

∴ ∠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°