Question

use the diagram to the right to find the measures of the angles listed below.

1. ∠ptq
2. ∠qtr
3. ∠pts
4. in order to find m∠qtr, begin by finding a sum or difference of angle measures that is equal to m∠qtr. which of the following expressions is equal to m∠qtr?

a. m∠rtp - m∠ptq
b. m∠rtp + m∠tpr
c. m∠rtp - m∠tpr
d. m∠rtp + m∠ptq
the measure of m∠rtp is . (type an integer or a decimal. do not include the degree symbol.)

Explanation:

Step1: Analyze angle - relationship for ∠QTR

From the diagram, we can see that ∠RTP is composed of ∠QTR and ∠PTQ. So, ∠QTR=∠RTP - ∠PTQ.

Step2: Identify the correct option

Based on the above - derived relationship, the correct expression for m∠QTR is m∠RTP - m∠PTQ. So the answer for the multiple - choice part is A.

Step3: Find m∠RTP

Since ∠RTP and the 50 - degree angle are vertical angles, vertical angles are equal. So m∠RTP = 50.

Answer:

A. m∠RTP - m∠PTQ
50