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2 years ago

PLEASE HELP ME. ILL OFFER MANY POINTS

Mathematics

1 answer:

Alina [70]2 years ago

7 0

Answer:

<h3> small angle: 24° ; middle angle: 72° ; large angle: 84°</h3>

Step-by-step explanation:

x - the smallest angle

3x - the middle angle

2x - twice the smallest angle

3·3x - 3 times the middle angle

twice the measure of the largest angle (the difference of 3 times the middle angle and twice the smallest angle): 3·3x - 2x = 7x

7x÷2 = 3.5x - the largest angle

The sum of angles in any triangle is 180°, so:

x + 3x + 3.5x = 180°

7.5x = 180° {divide both sides by 7.5}

x = 24°

small angle: x = 24°

middle angle: 3x = 3·24° = 72°

large angle: 3.5·24° = 84°

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Given Information :-

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A polygon with 10 sides ( Decagon )

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To Find :-

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The value of one of the exterior angles

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Formula Used :-

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$\qquad \diamond \: \underline{ \boxed{ \pink{ \sf Exterior ~angle = \dfrac {360^\circ}{no. ~of~sides}}}} \: \star$

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Solution :-

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Putting the given values, we get,

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$\sf \dashrightarrow Exterior ~angle = \dfrac{360 ^\circ}{10} \: \: \\ \\ \\ \sf \dashrightarrow Exterior ~angle = \frac{36 \cancel{0}^\circ}{ \cancel{10}} \: \: \\ \\ \\ \sf \dashrightarrow Exterior ~angle = \underline{ \boxed{ \frak{ \red{36^\circ}}}} \: \star \\ \\$

Thus, the value of the exterior angles of a Decagon is 36°.

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$\underline{ \rule{227pt}{2pt}} \\ \\$

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