The diagonals of a rectangle ABCD meet at O, If ∠BOC = 44°, find ∠OAD. The rectangle ABCD is given as: We have, ∠BOC +∠BOA = 180° (Linear pair) 44° +∠BOA = 180° ∠BOA = 180° -44° ∠BOA = 136° Since, diagonals of a rectangle are equal and they bisect each other. Therefore, in ΔOAB, we have OA = OB (Angles opposite to equal sides are equal.) Therefore, ∠1 = ∠2 Now,in ΔOAB, we have ∠BOA + ∠1 +∠2 = 180 ∠BOA + 2∠1 = 180° 2∠1 = 44° ∠1 = 22° Since, each angle of a rectangle is a right angle. Therefore, ∠BAD = 90° ∠1+∠3 = 90° 22° +∠3 = 90° ∠3 = 68° Thus, ∠OAD = 68° Hence, the measure of∠OAD is 68°. Concept: Angle Sum Property of a Quadrilateral Is there an error in this question or solution? Open in App In rectangle ABCD, ∠AOD=44∘ [vertically opposite] ∠ODA=∠OAD=x∘ [Since ΔOAD is an isosceles triangle) ∴ By the angle sum property of a triangle, we have ⇒∠OAD + ∠ODA + ∠AOD = 180∘ ⇒x∘+x∘+44∘=180∘ ⇒2x∘+44∘=180∘ ⇒x∘=180∘−44∘2=136∘2=68∘ ∴∠OAD=68∘ Suggest Corrections |