Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![### Finding the Measure of the Missing Angle
In this problem, we are asked to find the measure of a missing angle in a given geometric figure.
#### Diagram Explanation
The diagram consists of two intersecting lines forming an angle at one of the intersection points with an adjacent right angle. One angle is labeled as \( 49^\circ \), and next to it, the missing angle is marked as \( a \).
#### Solving the Problem
Given that one of the adjacent angles is \( 49^\circ \) and the small square indicates that the other adjacent angle is a right angle \( 90^\circ \), we can find the measure of angle \( a \) using the following concept:
- The sum of angles on a straight line is \( 180^\circ \).
- The right angle provided is \( 90^\circ \).
Therefore, the angle \( a \) can be calculated as follows:
\[ a = 90^\circ - 49^\circ = 41^\circ \]
#### Answer
Thus, the measure of the missing angle \( a \) is:
\[ a = 41^\circ \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a69dae7-0d19-46aa-887a-d0111e94c36c%2Fbc7965aa-911a-4762-b67e-9136be03765b%2Fekzhlo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Measure of the Missing Angle
In this problem, we are asked to find the measure of a missing angle in a given geometric figure.
#### Diagram Explanation
The diagram consists of two intersecting lines forming an angle at one of the intersection points with an adjacent right angle. One angle is labeled as \( 49^\circ \), and next to it, the missing angle is marked as \( a \).
#### Solving the Problem
Given that one of the adjacent angles is \( 49^\circ \) and the small square indicates that the other adjacent angle is a right angle \( 90^\circ \), we can find the measure of angle \( a \) using the following concept:
- The sum of angles on a straight line is \( 180^\circ \).
- The right angle provided is \( 90^\circ \).
Therefore, the angle \( a \) can be calculated as follows:
\[ a = 90^\circ - 49^\circ = 41^\circ \]
#### Answer
Thus, the measure of the missing angle \( a \) is:
\[ a = 41^\circ \]
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