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Five of the interior angles of a hexagon are 90°, 100°, 110°, 120° and 130°.
a Work out the other interior angle of the hexagon.
b Calculate the external angles of the hexagon and show that they have the correct tota

Sagot :

Answer:

see explanation

Step-by-step explanation:

The sum of the interior angles of a polygon is

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

here n = 6 ( sides of a hexagon ) , then

sum = 180° × 4 = 720°

(a)

let x be the sixth interior angle , then

90° + 100° + 110° + 120° + 130° + x = 720 , that is

550° + x = 720° ( subtract 550° from both sides )

x = 170°

(b)

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

exterior angle + interior angle = 180°

exterior angle = 180° - interior angle

Then

180° - 90° = 90°

180° - 100° = 80°

180° - 110° = 70°

180° - 120° = 60°

180° - 130° = 50°

180° - 170° = 10°

sum = 90° + 80° + 70° + 60° + 50° + 10° = 360° ← correct total

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