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Question
In rectangle READ, find ∠EAR, ∠RAD and ∠ROD
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Solution
Given, READ is a rectangle in which the diagonals ED and AR intersect at O.
We have, ROA is a straight line
So, ∠ROE + ∠EOA = 180°
`\implies` ∠EOA = 180° – 60°
`\implies` ∠EOA = 120° ...(i)
In ΔOEA, OE = OA ...[∵ Diagonals of a rectangle are equal and they bisect each other]
`\implies` ∠OEA = ∠OAE = x ...(Say)
And ∠OEA + ∠EAO + ∠AOE = 180° ...[Angle sum property]
`\implies` x + x + 120° = 180° ...[From (i)]
`\implies` 2x = 60°
`\implies` x = 30°
∴ ∠EAO = 30°
`\implies` ∠EAR = 30°
Now, ∠RAD = ∠EAD – ∠EAR
= 90° – 30° ...[∵ ∠A = 90°]
= 60°
As ∠EOA = ∠DOR = 120° ...[∵ Vertically opposite angles]
Hence, ∠EAR = 30°, ∠RAD = 60° and ∠ROD = 120°
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