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The exterior angles of a hexagon are in the ratio 1:2:4:5:8:10. Then the interior angles of the hexagon are

a. 169, 158, 136, 125, 92 and 70
b. 168, 156, 132, 120, 84 and 60
c. 167, 154, 128, 115, 76 and 50
d. 166, 152, 124, 110, 68 and 40

User Shante
by
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1 Answer

2 votes

Answer:

B

Explanation:

the sum of the exterior angles of a polygon is 360°

sum the parts of the ratios, 1 + 2 + 4 + 5 + 8 + 10 = 30 parts

divide 360° by the number of parts to find the value of one part of the ratio.

360° ÷ 30 = 12° , then

2 parts = 2 × 12° = 24°

4 parts = 4 ° 12° = 48°

5 parts = 5 × 12° = 60°

8 parts = 8 × 12° = 96°

10 parts = 10 × 12° = 120°

the 6 exterior angles are 12° , 24° , 48° , 60° , 96° , 120°

then in a polygon

interior angle + exterior angle = 180° ( subtract exterior angle from both sides )

interior angle = 180° - exterior angle

using the above 6 exterior angles

12° : interior angle = 180° - 12° = 168°

24° : interior angle = 180° - 24° = 156°

48° : interior angle = 180° - 48° = 132°

60° : interior angle = 180° - 60° = 120°

96° : interior angle = 180° - 96° = 84°

120° : interior angle = 180° - 120° = 60°

the 6 interior angles are 168° , 156° , 132° , 120° , 84° , 60°

User IamAshay
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