ABCD is a rectangle. E is a point on AB such that AD $=$ AE. Find x and y.
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Given :

ABCD is a rectangle.

AD $=$ AE.

To do :

We have to find x and y.

Solution :

ABCD is a rectangle.

$∠A = ∠B = ∠C = ∠D = 90°$

E is a point on AB such that $AD = AE$.

In the triangle ADE,

$AD = AE$

We know that,

Angles opposite to equal sides are equal.

Therefore,

$∠ADE = ∠AED$

$∠ADE + ∠AED + 90° = 180°$

$2∠ADE = 180°-90° = 90°$

$∠ADE = \frac{90°}{2} = 45°$.

$∠ADE = ∠AED = 45°$.

$∠AED + ∠y = 180°$               (Sum of the angles on a straight line is 180°)

$45° + ∠y = 180°$

$∠y = 180°-45° = 135°$

$∠ADE + ∠x = 90°$

$45 + ∠x = 90°$

$∠x = 90°-45° = 45°$

The measures of the angles x and y are 45° and 135°.

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Updated on: 10-Oct-2022

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