How do you sketch the angle 235 degrees and find its reference angle?

Apr 2, 2018

Reference Angle of ${235}^{\circ}$ is ${55}^{\circ}$.

Explanation:

Given:

The angle given is $\angle B A C = {235}^{\circ}$ (in the counterclockwise direction).

The reference angle is the angle that the given angle makes with the x-axis.

Regardless of where the angle ends, the reference angle measures the closest distance of that terminal side to the x-axis.

In the picture that follows, $\alpha$ is the given angle in the standard position.

Reference angle is the acute angle formed by the terminal side of $\alpha$ and the x-axis.

$\beta$ is the reference angle.

$\angle D A C = {55}^{\circ}$ is the required reference angle.

To verify our result, we can graph the angle in the standard position and the reference angle using a software as shown: