Question

How can I solve this mission measurement angle with a supplement angle?

Answer 1

158.6 °

Step-by-step explanation

Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

So

Step 1

Let

`\begin{gathered} \text{angle}1=\angle QON \\ \text{angle}2=\angle QOP \\ as\text{ the angles are supplem} \\ \text{angle}1+angle2=180 \\ \text{replacing} \\ \angle QON+\angle QOP=180 \\ 21.4\text{ \degree+}\angle QOP=180 \end{gathered}`

Step 2

Finally, let's solve for angle QOP

`\begin{gathered} 21.4\text{ \degree+}\angle QOP=180 \\ \text{subtract 21.4 \degree in both sides} \\ 21.4\text{ \degree+}\angle QOP=180-21.4\~=180-21.4 \\ \angle QOP=158.6\text{ \degree} \\ \angle QOP=158.6\text{ degr}ees \end{gathered}`

so, the supplementary angle of 21.4 is 158.6 degrees

I hope this helps you