Question

The two angle of the quadrilateralmeasure 60 degree and 90 degree and the other two angles are equal.find the measure of the two angles.​

Answer 1

Question : The two angles of the quadrilateral measure 60 degree and 90 degree and the other two angles are equal. Find the measure of the two angles.

Solution :

$\bold {Given :}$

• Measure of two angles of the quadrilateral = 60° and 90°

$\bold {To \:Find}$

• The measure of the two equal angles.

Let the measure of the two equal angles be x° .

Atq,

$\boxed{\blue {Sum\: of \:all\: angles\: of\: quadrilateral = 360^{\circ}}}$

$\implies 60 + 90+ x + x = 360 \\ \implies 150 + 2x = 360 \\ \implies 2x= 360-150 \\\implies 2x =210\\ \implies x= \frac{210}{2} \\ \implies x= 105$

$\boxed{\green {Hence,\:the\: measure\: of\: the\: two \:equal\: angles = 105^{\circ}}}$

$\bold{Verification :}$

$\implies 60^{\circ}+90^{\circ}+105^{\circ}+105^{\circ}=360^{\circ}\\ \implies 150^{\circ}+210^{\circ}=360^{\circ}\\ \implies 360^{\circ}=360^{\circ}\\ \implies LHS=RHS$

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Answer 2

Given ,

The two angles of quadrilateral are 60°

and 90° and the other two angles are equal

Let , the other angle be x

We know that , the sum of angles of quadrilateral is 360°

So ,

=> 60 + 90 + x + x = 360

=> 60 + 90 + 2x = 360

=> 150 + 2x = 360

=> 2x = 360 - 150

=> 2x = 210

=> x = 210/2

=> x = 105

Hence , the other two angles are 105° and 105°

__________________________

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