Question

The two angles of a quadrilateral are 87° and 77° . If the two angle are equal, find their measures.​

Answer 1

Answer:

98°. Measure of each equal angle is 98°.

Step-by-step explanation:

Let the measure of each equal angle be x.

We know, sum of all angles in an quadrilateral is 360°.

Sum of all angles = 360°

87° + 77° + x + x = 360°

184° + 2x = 360°

2x = 360° - 184°

2x = 196°

x = 196/2 = 98°

The required angles are 98° and 98°.

Answer 2

Answer:

Given :-

• The two angles of a quadrilateral are 87° and 77°. If the two angles are equal.

To Find :-

• What is the measures of angles.

Solution :-

Let,

$\mapsto$ First angle = x

$\mapsto$ Other angles will be = x

As we know that,

$\bigstar\: \: \sf\boxed{\bold{\pink{Sum\: of\: all\: angles\: of\: quadrilateral =\: 360^{\circ}}}}$

According to the question,

$\implies \sf 87^{\circ} + 77^{\circ} + x + x =\: 360^{\circ}$

$\implies \sf 164^{\circ} + x + x =\: 360^{\circ}$

$\implies \sf 164^{\circ} + 2x =\: 360^{\circ}$

$\implies \sf 2x =\: 360^{\circ} - 164^{\circ}$

$\implies \sf 2x =\: 196^{\circ}$

$\implies \sf x =\: \dfrac{\cancel{196^{\circ}}}{\cancel{2}}$

$\implies \sf x =\: \dfrac{98^{\circ}}{1}$

$\implies \sf\bold{\purple{x =\: 98^{\circ}}}$

Hence, the required angles of quadrilateral are :

$\bullet\: \: \rm{\bold{\red{First\: angle =\: 98^{\circ}}}}$

$\bullet\: \: \rm{\bold{\red{Other\: angle =\: 98^{\circ}}}}$

$\therefore$ The measures of other two angles of a quadrilateral is 98° and 98° respectively.

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VERIFICATION :-

$\longrightarrow \tt{87^{\circ} + 77^{\circ} + x + x =\: 360^{\circ}}$

By putting x = 98° we get,

$\longrightarrow \tt{87^{\circ} + 77^{\circ} + 98^{\circ} + 98^{\circ} =\: 360^{\circ}}$

$\longrightarrow \tt{164^{\circ} + 196^{\circ} =\: 360^{\circ}}$

$\longrightarrow \tt{\bold{\green{360^{\circ} =\: 360^{\circ}}}}$

Hence, Verified.

EXTRA INFORMATION :-

$\mapsto$ Quadrilateral :

• A polygon with four sides is called quadrilateral.
• The sum of the measures of four angles of a quadrilateral is 360° .