four angles of a pentagon are equal and the fifth angle is 160°. find the measure of each of the equal angle.
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four angles of a pentagon are equal and the fifth angle is 160°. find the measure of each of the equal angle.
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Given:-
To find:-
Solution:-
As we know that ,
[tex]\red{\boxed{\sf Sum \: of \: 5 \: angles \: in \: a \: pentagon \: is \: {540}^{\circ}}}[/tex]
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° = 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°
Answer:
95°
Step-by-step explanation:
Given:-
To find:-
Measure of each equal angle .
Solution:-
Let the unknown angles be x
We know that in a pentagon
[tex]{\color{navy}{\boxed{\blue{\boxed{\gray{\sf Sum\:of\:angles=540°}}}}}}[/tex]
ATQ
[tex]\\ \sf {:}\longrightarrow x+x+x+x+160=540[/tex]
[tex]\\ \sf {:}\longrightarrow 4x+160=540[/tex]
[tex]\\ \sf {:}\longrightarrow 4x=540-160[/tex]
[tex]\\ \sf {:}\longrightarrow 4x=380[/tex]
[tex]\\ \sf {:}\longrightarrow x=\dfrac{380}{4}[/tex]
[tex]\\ \sf {:}\longrightarrow x=95°[/tex]
Know more:-
[tex]{\color{navy}{\boxed{\blue{\boxed{\color{black}{\sf Sum\:of\: interior\:angles\;of\:a\:Polygon=(n-2)\times 180^{\circ}}}}}}}[/tex]