Question

please give me correct answer​

Answer 1

Answer :-

• 165°.

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⋆Question :-

• The four angles of a pentagon are 40°, 75° , 125° and 135° . The measure of the fifth angle is :-

1. 165°
2. 170°
3. 160°
4. 175°

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Answer :-

• The four angles of a pentagon are 40°, 75° , 125° and 135° . The measure of the fifth angle is :-

1. 165° ✔
2. 170°
3. 160°
4. 175°

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Given :-

• Four angles of a pentagon (Five sided figure) that are 40°, 75° , 125° and 135°

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Find :-

• Fifth angle of the pentagon .

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We know :-

• Sum of interior angles of pentagon is 540° .

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⋆Solution :-

Let the fifth angle be X .

∴ X + 40° + 75° + 125° + 235° = 540° [Sum of interior angles of pentagon is 540° ].

⟹ X + 375° = 540°

⟹ X = 540° - 375°

⟹ X = 165° .

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Regular Polygon Name Each

interior angle

• Triangle • 60°
• Quadrilateral • 90°
• Pentagon • 108°
• Hexagon • 120°
• Septagon • 128 . 57°
• Octagon • 135°
• Nonagon • 140°
• Decagon • 144°

☆Note :- It is written each interior angle and not all . So, Don't be confused by seeing that pentagon is 540° , then how here it is 108° . It I because in 540° we multiplied 5 with 108° see 108° multiply 5 = 540° .

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How , 540° came :-

We know it is pentagon that means which has 5 sides .

So, let

n be No. of sides then, Using the formula

Sum of all angles of a Polygon

➨2n-4 ✖ 90°

Here , n = 5

➨2✖5 -4 ✖ 90°

➨10-4✖90°

➨6✖90°

➨ 540°