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The angles of a pentagon are x, x − 5

, x + 10
, 2x + 15and 2x + 30

. Find all the angles.

User CoolBots
by
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1 Answer

3 votes

Answer:

65°, 70°, 80°, 155°, 170°

Explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

here n = 5 ( pentagon )

sum = 180° × 3 = 540°

Sum the given angles and equate to 540

x + x - 5 + x + 10 + 2x + 15 + 2x + 30 = 540

7x + 50 = 540 ( subtract 50 from both sides )

7x = 490 ( divide both sides by 7 )

x = 70

Hence angles are

x = 70°

x - 5 = 70 - 5 = 65°

x + 10 = 7 0 + 10 = 80°

2x + 15 = (2 × 70) + 15 = 140 + 15 = 155°

2x + 30 = (2 × 70) + 30 = 140 + 30 = 170°

User Dude Dawg
by
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