Question

in quadrilateral ABCD ,side BC parallel side AD ,side AB congruent side DC if angle A =72degree then find the measure of angle B and angle D i want urgent...​

Answer 1

Step-by-step explanation:

∠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°Read more on Sarthaks.com - https://www.sarthaks.com/850363/in-quadrilateral-abcd-side-bc-side-ad-side-ab-side-dc-if-a-72-then-find-the-measures-of-b-and