Lines t1, t2, and t3 are parallel lines intersected by line t4. What is the measure of Zp? 20. 44° ta A. 44° B. 134° C. 136° D. Not enough information.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Question 20:**

Lines \(t_1\), \(t_2\), and \(t_3\) are parallel lines intersected by line \(t_4\). What is the measure of ∠ \(p\)?

The diagram associated with the question shows three horizontal parallel lines, labeled \(t_1\), \(t_2\), and \(t_3\). These lines are intersected by a diagonal line \(t_4\). The point of intersection between \(t_4\) and \(t_3\) forms an angle of 44° on the lower right side of \(t_4\), and the point of intersection between \(t_4\) and \(t_1\) forms an angle designated as ∠ \(p\) on the upper left side of \(t_4\).

Given Options:
A. 44°
B. 134°
C. 136°
D. Not enough information.

**Answer Explanation:**

To determine the measure of ∠ \(p\), we use the properties of parallel lines cut by a transversal. When a transversal intersects parallel lines, alternate interior angles are congruent. Therefore, if one angle formed by the intersection of \(t_4\) and \(t_3\) is 44°, then the alternate interior angle formed by the intersection of \(t_4\) and \(t_1\) (which is ∠ \(p\)) is also 44°.

Correct Answer: 
**A. 44°**
Transcribed Image Text:**Question 20:** Lines \(t_1\), \(t_2\), and \(t_3\) are parallel lines intersected by line \(t_4\). What is the measure of ∠ \(p\)? The diagram associated with the question shows three horizontal parallel lines, labeled \(t_1\), \(t_2\), and \(t_3\). These lines are intersected by a diagonal line \(t_4\). The point of intersection between \(t_4\) and \(t_3\) forms an angle of 44° on the lower right side of \(t_4\), and the point of intersection between \(t_4\) and \(t_1\) forms an angle designated as ∠ \(p\) on the upper left side of \(t_4\). Given Options: A. 44° B. 134° C. 136° D. Not enough information. **Answer Explanation:** To determine the measure of ∠ \(p\), we use the properties of parallel lines cut by a transversal. When a transversal intersects parallel lines, alternate interior angles are congruent. Therefore, if one angle formed by the intersection of \(t_4\) and \(t_3\) is 44°, then the alternate interior angle formed by the intersection of \(t_4\) and \(t_1\) (which is ∠ \(p\)) is also 44°. Correct Answer: **A. 44°**
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