Question

use the figure shown for exercises 10–13. 10. what is ( mangle ptr )? 11. what is ( mangle ptq )? 12. what is ( mangle qts )? 13. understand luis said that ( mangle qtr = 80^circ ). explain luis’s error.

Explanation:

Question 10: What is \( m\angle PTR \)?

Step 1: Identify the angle on the protractor

Looking at the protractor, ray \( TR \) is at \( 90^\circ \) from the horizontal ray \( TP \) (since it's a right angle or the protractor shows \( 90^\circ \) for \( \angle PTR \)).
\( m\angle PTR = 90^\circ \)

Step 1: Read the protractor for \( \angle PTQ \)

From the protractor, ray \( TQ \) is at \( 60^\circ \) from \( TP \). So the measure of \( \angle PTQ \) is the angle between \( TP \) and \( TQ \), which is \( 60^\circ \).
\( m\angle PTQ = 60^\circ \)

Step 1: Find \( m\angle PTS \) and \( m\angle PTQ \)

First, \( m\angle PTS \) is \( 120^\circ \) (from protractor, ray \( TS \) is at \( 120^\circ \) from \( TP \)) and \( m\angle PTQ = 60^\circ \) (from question 11).

Step 2: Calculate \( m\angle QTS \)

\( m\angle QTS = m\angle PTS - m\angle PTQ \)
\( m\angle QTS = 120^\circ - 60^\circ = 60^\circ \)

Answer:

\( 90^\circ \)

Question 11: What is \( m\angle PTQ \)?