Question
Find the measure of a complementary angle, a supplementary angle, and a vertical angle for the following measures. Complete parts (a) and (b) below.
Identify the measure of a supplementary angle of
The measure of the supplement is
(Simplify your answer.)
Identify the measure of a vertical angle of
The measure of the vertical angle of
(Simplify your answer.)
b. m(
Identify the measure of a complementary angle of
The measure of the complement is
(Simplify your answer.)
Identify the measure of a supplementary angle of
The measure of the supplement is
(Simplify your answer.)
Identify the measure of a vertical angle of
The measure of the vertical angle of
Identify the measure of a supplementary angle of
The measure of the supplement is
(Simplify your answer.)
Identify the measure of a vertical angle of
The measure of the vertical angle of
(Simplify your answer.)
b. m(
Identify the measure of a complementary angle of
The measure of the complement is
(Simplify your answer.)
Identify the measure of a supplementary angle of
The measure of the supplement is
(Simplify your answer.)
Identify the measure of a vertical angle of
The measure of the vertical angle of
Ask by Rose Lindsey. in the United States
Mar 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
-
For
: - Complementary angle:
- Supplementary angle:
- Vertical angle:
- Complementary angle:
-
For
: - Complementary angle:
- Supplementary angle:
- Vertical angle:
- Complementary angle:
Solution
Let’s break down the problem step by step.
Part (a)
-
Complementary Angle:
- The measure of a complementary angle is calculated as:
- Given
: - Therefore, the measure of the complementary angle is
.
- The measure of a complementary angle is calculated as:
-
Supplementary Angle:
- The measure of a supplementary angle is calculated as:
- Given
: - Therefore, the measure of the supplementary angle is
.
- The measure of a supplementary angle is calculated as:
-
Vertical Angle:
- Vertical angles are equal to each other. Therefore, the measure of the vertical angle of
is: - Thus, the measure of the vertical angle is
.
- Vertical angles are equal to each other. Therefore, the measure of the vertical angle of
Part (b)
-
Complementary Angle:
- The measure of a complementary angle for
is: - Therefore, the measure of the complementary angle is
.
- The measure of a complementary angle for
-
Supplementary Angle:
- The measure of a supplementary angle for
is: - Therefore, the measure of the supplementary angle is
.
- The measure of a supplementary angle for
-
Vertical Angle:
- Similar to part (a), the measure of the vertical angle of
is equal to : - Thus, the measure of the vertical angle is
.
- Similar to part (a), the measure of the vertical angle of
Summary of Results
-
For
: - Complementary angle:
- Supplementary angle:
- Vertical angle:
- Complementary angle:
-
For
: - Complementary angle:
- Supplementary angle:
- Vertical angle:
- Complementary angle:
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
Did you know that the concepts of complementary and supplementary angles date back to ancient civilizations? The Greeks and Romans not only used these ideas in architecture and art but also created intricate mathematical theories around them! Aristotle even pondered the nature of angles, which laid the groundwork for many geometric principles we use today. So, the next time you calculate angles, remember you’re tapping into thousands of years of knowledge!
When it comes to real-world applications, understanding angles is crucial! Architects and engineers rely on complementary and supplementary angles to create stable structures, ensuring everything fits together perfectly. Even graphic designers use angle measurements to achieve the right proportions in their artwork. Whether you’re building a treehouse or designing a website, angles play a significant role in making things functional and aesthetically pleasing. So, embrace your inner architect!
