Question

In rectangle READ, find ∠EAR, ∠RAD and ∠ROD

Answer 1

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°