Question

The two angles of a quadrilateral are 90° each, and the other two angles are such that one of them
is twice the other. Find the angles.​

Answer 1

Answer:

Angle sum of quadrilateral = 360

Two angles = 90° and 90°

let other one angle be x

fourth angle = 2x

by the given condition:

90° + 90° + x + 2x = 360°

180° + 3x = 360°

3x = 360° - 180° = 180°

x = 180°/3 = 60°

one angle = 60°

fourth angle = 120°

hope this helps!

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Answer 2

$</p><p>{\bold{\underline{\underline{Answer:}}}}$

$</p><p>{\bold{\therefore \angle C=60\degree}}$

$</p><p>{\bold{\therefore \angle D=120\degree}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\bold{Let \: Quadrilateral \: be \: ABCD : } \\ \\ \underline \bold{Given : } \\ \implies \angle A = 90 \degree \\ \\ \implies \angle B = 90 \degree \\ \\ \underline \bold{To \: Find : } \\ \implies \angle C = ? \\ \\ \implies \angle D= ?$

• According to given question :

$\bold{Let \: \angle C= x : } \\ \: \: \: \: \: \: \bold{ \angle D= 2x} \\ \\ \bold{Using \: property \: of \: Quadrilateral : } \\ \implies \angle A + \angle B + \angle C+ \angle D= 360 \degree \\ \\ \implies 90 + 90 + x + 2x = 360 \\ \\ \implies 180 + 3x = 360 \\ \\ \implies 3x = 360 - 180 \\ \\ \implies 3x = 180 \\ \\ \implies x = \frac{\cancel{180}}{\cancel3} \\ \\ \bold{\implies x = 60 \degree} \\ \\ \bold{ \therefore\angle C= x = 60 \degree} \\ \bold{ \therefore\angle D= 2x = 120 \degree}$