Question

four angles of a pentagon are equal and the fifth angle is 160°. find the measure of each of the equal angle.​

Answer 1

Given:-

• The four angles in a pentagon are equal
• 5th angle of a pentagon is 160°

To find:-

• The measure of each of equal angles

Solution:-

As we know that ,

$\red{\boxed{\sf Sum \: of \: 5 \: angles \: in \: a \: pentagon \: is \: {540}^{\circ}}}$

ATQ four angles are equal that means Let the 4 angles are

x , x , x , x

And 5th angle is 160° So,

x + x + x + x + 160° = 540° [Sum of 5 angles in pentagon is 540°]

4x + 160° = 540°

4x = 540°-160°

4x = 380°

x = 380°/4

x = 95°

So, the each of equal 4 angles are 95°,95°,95°,95°

Verification:-

We know five angles in a pentagon since their sum should be 540°

• 95°
• 95°
• 95°
• 95°
• 160°

95° + 95° +95° + 95° + 160° = 540°

95°(4) + 160°= 540°

380° + 160° = 540°

540° = 540°

Hence verified !

___________________

Know more :-

☆Sum of angles in a Triangle is 180°

☆Sum of angles in a Quadrilateral is 360°

☆ Sum of angles in Pentagon is 540°

☆ Sum of angles in Hexagon is 720°

☆ Sum of angles in a Septagon is 900°

☆ Sum of angles in a Octogon is 1080°

☆ Sum of angles in a Nonagon is 1260°

Sum of angles in any polygon is

(n-2) 180°

• n = no.of sides

Answer 2

Answer:

95°

Step-by-step explanation:

Given:-

• Four angles of a pentagon are equal
• The fifth angle is 160°

To find:-

Measure of each equal angle .

Solution:-

Let the unknown angles be x

We know that in a pentagon

${\color{navy}{\boxed{\blue{\boxed{\gray{\sf Sum\:of\:angles=540°}}}}}}$

ATQ

$\\ \sf {:}\longrightarrow x+x+x+x+160=540$

$\\ \sf {:}\longrightarrow 4x+160=540$

$\\ \sf {:}\longrightarrow 4x=540-160$

$\\ \sf {:}\longrightarrow 4x=380$

$\\ \sf {:}\longrightarrow x=\dfrac{380}{4}$

$\\ \sf {:}\longrightarrow x=95°$

Know more:-

• If sides of a Polygon be n then

${\color{navy}{\boxed{\blue{\boxed{\color{black}{\sf Sum\:of\: interior\:angles\;of\:a\:Polygon=(n-2)\times 180^{\circ}}}}}}}$