Question

Two of the interior angles of a hexagon are 112° and 63°. the exterior angles of those angles are labelled a and b respectively. Find the sum of other exterior angles of the hexagon excluded the angles of a and b.

Answer 1

The followings are the property of a polygon:

• $\text{Sum of interior angles} = (n - 2) \times 180$
• $\text {Sum of external angles} = 360$
• $\text{internal angle} + \text{corresponding external angle} = 180$

Also:

• A hexagon is a 6-sided polygon

Given:

Two of the interior angles are 112° and 63°

Find the sum of the two exterior angles:

corresponding external angle of 112 = 180 - 112

corresponding external angle of 112 = 68°

corresponding external angle of 63 = 180 - 63

corresponding external angle of 112 = 117°

Sum of the two external angles = 68 + 117

Sum of the two external angles = 185°

Find the sum of the exterior angles excluding these 2 angles:

Sum of the rest of the external angles = 360 - 185

Sum of the rest of the external angles = 175°

Answer: 175°

Answer 2

Two of the interior angles of a hexagon are 112° and 63°. the exterior angles of those angles are labelled a and b respectively. The sum of other exterior angles of the hexagon excluded the angles of a and b is 175°.

Stepwise explanation is given below:

- A hexagon is a 6-sided polygon

It is given that the

- Two of the interior angles are 112° and 63°

We need to find the sum of the two exterior angles:

corresponding external angle of 112°

= 180 - 112 = 68°

corresponding external angle of 63°

= 180 - 63= 117°

- Sum of the two external angles

= 68 + 117= 185°

- The sum of the exterior angles excluding these 2 angles:

- Sum of the rest of the external angles = 360 - 185 = 175°