Question

If the given figure ABCD is a square. Find the measure of ∠CAD

Answer 1

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Given,

ABCD is a square.

In Δ ADC,

AD = DC [All sides of square are equal]

=> ∠CAD = ∠ACD

Angle opposite to equal sides are equal in a Δ.

•°• ∠CAD = ∠ACD = x°

To find :- ∠CAD

By Angle Sum Property of Δ

•°•∠CAD + ∠ACD +∠ ADC = 180°

=> x° + x° + 90° = 180°

=> 2x° = 180° - 90°

= > 2x° = 90°

=> x° = 90°/2

=> x° = 45°

Hence, ∠CAD = 45°

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Answer 2

Solution ;

In the given square :-

DA = AC

Angle ACD = Angle DCA

Let the angles C and A be 'X'

Now ,

➨ X + X + 90° = 180°

➨ 2X + 90° = 180°

➨ 2X = 180° - 90°

➨ 2X = 90°

➨ X = 90/2 = 45°

Hence ,

Angle CAD = 45°