Question

Two of the exterior angles of a triangle are $158^\circ$ and $99^\circ.$ Find the third exterior angle, in degrees.

Answer 1

The third exterior angle is
`103^o`

Explanation:

Given

`\theta = 158^o`

`\alpha = 99^o`

Required

The third exterior angle
`(\beta)`

The exterior angles of a triangle add up to 360 degrees.

So:

`\theta + \alpha + \beta = 360^o`

Make
`\beta` the subject

`\beta = 360^o - (\theta + \alpha)`

Substitute known values

`\beta = 360^o - (158^o + 99^o)`

`\beta = 103^o`