Question

in a quadrilateral, the measure one angle is 87° if the measure of the other three angles are equal find the measure of remaining angle of a quadrilateral​

Answer 1

Answer:

The measure of all three angles is 91° each.

Step-by-step explanation:

Given measure of one angle of quadrilateral is 87°

Sum of four angles of quadrilateral is 360°

If X be the remaining angle (all angles are equal),

87+ 3X= 360

3X= 360-87

3X= 273

x=273/3= 91°

The measure of all three angles is 91° each.

This is the required answer.

Answer 2

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,

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

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 :

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

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

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

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

VERIFICATION :-

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

By putting x = 98° we get,

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

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

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

$\mathfrak{Hence, Verified}$

$\begin{gathered}\\\end{gathered}$

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° .