Question

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

Answer 1

The missing interior angle of the hexagon is 170°. The external angles of the hexagon do not have the correct total. The sum of the external angles should be 360°.

Step-by-step explanation:

To find the other interior angle of the hexagon, we need to know that the sum of all interior angles of a hexagon is always 720°. Since we already know 5 of the interior angles, we can find the missing angle by subtracting the sum of those angles from 720°.

Sum of given angles: 90° + 100° + 110° + 120° + 130° = 550°

Missing angle: 720° - 550° = 170°

Therefore, the missing interior angle of the hexagon is 170°.

To calculate the external angles of the hexagon, we need to know that the sum of all external angles of any polygon is always 360°. The external angle of a polygon is supplementary to its corresponding interior angle.

So, the external angle of the hexagon is 180° - 90° = 90°.

To show that the external angles have the correct total, we can find the sum of all external angles of the hexagon and verify that it is equal to 360°.

Total external angles: 90° + 90° + 90° + 90° + 90° = 450°

Since the total is not equal to 360°, there might be an error in the given angles or calculation.

Answer 2

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