Question

Complete. You may find that drawing a diagram will help you.

If$\angle POQ$is a straight angle and Ris any point not on $\overleftrightarrow{PQ}$, then$m\angle$___?___+$m\angle$___?___= ___?___.

Short answer

If $\angle POQ$ is a straight angle and R is any point not on $\overleftrightarrow{PQ}$, then $m\angle POR+m\angle ROQ={180}^0$.

Step-by-step solution

Step 1. State the concept used.

• The straight angle measures ${180}^0$.
• Angle addition postulate: The Angle addition postulate states that if two angles are placed side by side, then the value of the resulting angle is equal to the sum of the original angles
• The angle formed by two side by side angles is the sum of their measures.

Step 2. Draw the diagram.

Draw the diagram with the point R not on $\overleftrightarrow{PQ}$and a straight angle $\angle POQ$.

Step 3. State the conclusion.

Using angle addition postulate,

$m\angle POR+m\angle ROQ=m\angle POQ$

And since,$\angle POQ$is a straight angle therefore, the measure of the angle will be ${180}^0$.

Hence, localid="1648791697962" $m\angle POR+m\angle ROQ={180}^0$.