Question

the reference angle of - 156° is
the reference angle of 323° is
the reference angle of 230° is

Explanation:

Step1: Find reference angle of \(230^{\circ}\)

Since \(230^{\circ}\) is in the third - quadrant (\(180^{\circ}<230^{\circ}<270^{\circ}\)), the reference angle \(\theta_{r}=230^{\circ}-180^{\circ}\)
\(\theta_{r}=50^{\circ}\)

Step2: Find reference angle of \(323^{\circ}\)

Since \(323^{\circ}\) is in the fourth - quadrant (\(270^{\circ}<323^{\circ}<360^{\circ}\)), the reference angle \(\theta_{r}=360^{\circ}-323^{\circ}\)
\(\theta_{r}=37^{\circ}\)

Step3: Find reference angle of \(- 156^{\circ}\)

First, find the positive coterminal angle of \(-156^{\circ}\). Add \(360^{\circ}\) to \(-156^{\circ}\), we get \(-156^{\circ}+360^{\circ}=204^{\circ}\)
Since \(204^{\circ}\) is in the third - quadrant (\(180^{\circ}<204^{\circ}<270^{\circ}\)), the reference angle \(\theta_{r}=204^{\circ}-180^{\circ}\)
\(\theta_{r}=24^{\circ}\)

Answer:

\(24\), \(37\), \(50\)