Question

ABHC is a trapeziumin in which AB || HC and ∆A =∆B =45°.Find angles C and H of the trapezium.​

Answer 1

$\sf\underbrace{Correct\:Question: }$

ABCD is a trapezium in which AB parallel to DC & angle A = Angle B = 45° . find the angles C & D of the trapezium.

$\sf\underbrace{Answer : }$

$\huge\bold{Given :}$

ABCD is a trapezium with AB || CD and angle A = angle B = 45°

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Since, adjacent angles ( Angle A and angle B ) are equal we can conclude that the trapezium ABCD is isoceles trapezium. Hence, Angle C would also be equal to angle D. so, let angle C = angle D be X.

$\bf\blue{By~angle~sum~property.}$

${: \implies}$ 45° + 45° + x + x = 360°

${: \implies}$2x + 90° = 360°

${: \implies}$2x = 360° - 90°

${: \implies}$2x = 270°

$\implies{\sf{\large {x \:\:\: \dfrac{270}{2}\: }}}$

　　　$\bf\green{x~=~135°}$

$\sf\underline{Hence,~angle~C~=~angle~D~=~135° }$