Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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

Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.