Find the measures of the angles marked x and y. Remember that (1) the sum of the measures of the angles of a triangle is 180° and (2) supplementary angles have a sum of 180°. y (2x+60)°
Find the measures of the angles marked x and y. Remember that (1) the sum of the measures of the angles of a triangle is 180° and (2) supplementary angles have a sum of 180°. y (2x+60)°
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
![**Homework: Section 3.3**
**Problem Statement:**
Find the measures of the angles marked \( x \) and \( y \). Remember that (1) the sum of the measures of the angles of a triangle is 180° and (2) supplementary angles have a sum of 180°.
**Diagram Explanation:**
In the image, there is a right triangle with one right angle marked. The other two angles are labeled \( x \) and \( y \). Outside the triangle, a linear pair of angles is shown, one being \( y \) and the other labeled \( (2x + 60)^\circ \).
**Equation Setup:**
1. For the triangle:
\[
x + y + 90 = 180
\]
\[
x + y = 90
\]
2. For the supplementary angles:
\[
y + (2x + 60) = 180
\]
\[
y + 2x + 60 = 180
\]
\[
y + 2x = 120
\]
**Solution:**
Solve the system of equations:
1. From \( x + y = 90 \):
\[
y = 90 - x
\]
2. Substitute into \( y + 2x = 120 \):
\[
(90 - x) + 2x = 120
\]
\[
90 + x = 120
\]
\[
x = 30
\]
3. Substitute back to find \( y \):
\[
y = 90 - 30 = 60
\]
**Final Answer:**
\( x = 30 \) and \( y = 60 \)
(Simplify your answer. Do not include the degree symbol in your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbab33270-041b-4950-9aab-1bd6479f5d03%2F516de51d-cda1-4964-b78e-444545c17d2b%2Fmc7d8mf.jpeg&w=3840&q=75)
Transcribed Image Text:**Homework: Section 3.3**
**Problem Statement:**
Find the measures of the angles marked \( x \) and \( y \). Remember that (1) the sum of the measures of the angles of a triangle is 180° and (2) supplementary angles have a sum of 180°.
**Diagram Explanation:**
In the image, there is a right triangle with one right angle marked. The other two angles are labeled \( x \) and \( y \). Outside the triangle, a linear pair of angles is shown, one being \( y \) and the other labeled \( (2x + 60)^\circ \).
**Equation Setup:**
1. For the triangle:
\[
x + y + 90 = 180
\]
\[
x + y = 90
\]
2. For the supplementary angles:
\[
y + (2x + 60) = 180
\]
\[
y + 2x + 60 = 180
\]
\[
y + 2x = 120
\]
**Solution:**
Solve the system of equations:
1. From \( x + y = 90 \):
\[
y = 90 - x
\]
2. Substitute into \( y + 2x = 120 \):
\[
(90 - x) + 2x = 120
\]
\[
90 + x = 120
\]
\[
x = 30
\]
3. Substitute back to find \( y \):
\[
y = 90 - 30 = 60
\]
**Final Answer:**
\( x = 30 \) and \( y = 60 \)
(Simplify your answer. Do not include the degree symbol in your answer.)
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