Question

The measure of angle 1 is 30°, and the measure of angle 2 is 110°.


What is the measure of angle 4?

Answer 1

Theorem:
The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.

Angle 4 is an exterior angle of the triangle.
Angles 1 and 2 are the remote interior angles of angle 4.


m<4 = m<1 + m<2

m<4 = 30 deg + 110 deg

m<4 = 140 deg

Answer 2

The sum of all angles in a triangle is 180°.
$\alpha = 30 \\ \beta = 110 \\ \alpha + \beta + \gamma = 180 \\ 30 + 110 + \gamma = 180 \\ \gamma = 180 - 30 - 110 \\ \gamma = 40$
Since the angles 3 and 4 form an extended angle we need to subtract the angle 3 from 180°.
Why 180°? An extended angle is 180°
$180 = \gamma + angle4 \\ angle4 = 180 - \gamma \\ angle4 = 180 - 40 \\ angle4 = 120$
So angle4 = 120°