Question

If three interior angles of a pentagon are 100 ,110 and 90 and if the other two angles are equal , find the equal angles.

Answer 1

Given :

• Three interior angles of a pentagon are 100,110 and 90

• Other two angles are equal

To Find :

• The equal angles

Solutions :

We know that no. of sides of a pentagon is 5 and

sum of exterior angles is 360°

In general, If there is a polygon of n sides, we can divide it into (n-2) triangles with a common vertex,then the sum of interior angles of polygon would be :

$\bigstar \large \boxed{ \sf \: (n - 2) \times {180}^{ \circ} }$

$\longrightarrow \sf \: (5 - 2) \times {180}^{ \circ}$

$\longrightarrow \sf \: 3 \times {180}^{ \circ}$

$\longrightarrow \sf {540}^{ \circ}$

Let the other two equal angles be x

According to the Question :

$\longrightarrow \sf \: x + x + {100}^{ \circ} + {110}^{\circ} + {90}^{\circ} = {540}^{\circ}$

$\longrightarrow \sf \: 2x + {300}^{\circ} = {540}^{\circ}$

$\longrightarrow \sf \: 2x = {540}^{\circ} - {300}^{\circ}$

$\longrightarrow \sf \: 2x = {240}^{\circ}$

$\longrightarrow \sf \: x = \cancel\dfrac {240}{2} ^{ \circ}$

$\longrightarrow \sf \: x = \large \boxed{ \red{ \sf \: {120}^{ \circ}}}$

Hence,other two angles are of 120° each

Verification :

$\longrightarrow \sf \: {120}^{ \circ} + {120}^{ \circ} + {100}^{ \circ} + {110}^{\circ} + {90}^{\circ} = {540}^{\circ}$

$\longrightarrow \sf {240}^{\circ} + {210}^{\circ} + {90}^{\circ} = {540}^{\circ}$

$\longrightarrow \sf {450}^{\circ} + {90}^{\circ} = {540}^{\circ}$

$\longrightarrow \sf {540}^{\circ} = {540}^{\circ}$

Hence,Verified!

Answer 2

AnSweR :-

Each Equal angles are 120°

GiVeN :-

• Three interior angles of a pentagon are 100 , 110 , and 90.

• Other two angles are equal.

To FiNd :-

• Other two equal angles

SoLuTiOn :-

We know that their is a formula to find sum of all interior angles in any polygons.

So the given polygon is pentagon which is made of 5 sides and three triangles

So,

Pentagon is bounded by 5 sides.

• Formula = (n - 2) × 180 , where n = no of sides

So,

Sum of Interior angles in a pentagon is:-

=> ( n - 2) × 180

=> ( 5 - 2) × 180

=> 3 × 180 = 540°

Now,

According to Question :-

Let equal angles be x

Then,

$= > 100 + 110 + 90 + x + x = 540 \\ \\ = > 300 + 2x = 540 \\ \\ = > 2x = 540 - 300 \\ \\ = > x = \frac{240}{2} = 120$

Hence each equal angles are :-

=> x = 120°

VERIFICATION :-

• Sum of all interior angles in pentagon = 540°

So,

=> 100° + 110° + 90° + x + x = 540°

=> 300° + 120° + 120° = 540°

=> 540° = 540°

Hence,

L. H. S. = R. H. S.

Hence,

VERIFIED.....