Question

the five angles of a Pentagon are in the ratio 5:6:7:8:10 find the angles​

Answer 1

$\huge\mathfrak{Answer:}$

$\large\underline{\sf{\blue{Given:}}}$

• We have been given a Pentagon
• Angles of Pentagon are given in the ratio 5:6:7:8:10

$\large\underline{\sf{\blue{To \: Find:}}}$

• We have to find all the angles of a given Pentagon

$\large\underline{\sf{\blue{Solution:}}}$

Given that Angles of Pentagon are in ratio 5:6:7:8:10

Let ABCDE be the given Pentagon

• ∠A = 5x
• ∠B = 6x
• ∠C = 7x
• ∠D = 8x
• ∠E = 10x

$\large\underline{\mathfrak{\red{Using \: Angle \: sum \: Property:}}}$

$\implies \boxed{\sf{Sum \: of \: Angles = 540} }$

$\implies \sf{5x + 6x + 7x + 8x + 10x = 540}$

$\implies \sf{36x = 540}$

$\implies \sf{x = \dfrac{540}{36}}$

$\implies \boxed{\sf{x = 15}}$

$\sf{}$

Angles of Pentagon are as follows :

∠A $\sf{= 5 \times 15 = 75}$

∠B $\sf{= 6 \times 15 = 90}$

∠C $\sf{= 7 \times 15 = 105}$

∠D $\sf{= 8 \times 15 = 120}$

∠E $\sf{= 10 \times 15 = 150}$

Hence angles of pentagon are 75, 90, 105, 120, 150 in succession

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$\LARGE\underline{\sf{\green{Verification:}}}$

• Sum of angles of pentagon
• Sum = 75 + 90 + 105 + 120 + 150
• Sum = 540
• Sum of angles of pentagon comes out to be 540

Hence Verified !!

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$\large\purple{\underline{\underline{\mathtt{Extra \: Information:}}}}$

• Pentagon is a polygon having 5 sides and angles. There are many types of pentagon such as : Regular or irregular Pentagon
• Sum of interior angles of pentagon is equal to 540
• If all the sides and all the angles of pentagon are equal then it is a regular polygon
• In regular polynomial the measure of interior angle is 108

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NOTE :

• The sum of interior angles of a polygon having n number of sides is given by :

• $\boxed{\sf{S = (n-2) \times 180}}$