Question
The measure of an angle is
. What is the measure of its complementary angle?
Ask by Ayala Conner. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The complementary angle is
.
Solution
-
Two angles are complementary if their sum is
. -
Let the complementary angle be
. Then, -
Solve for
by subtracting from both sides: -
Compute the difference:
Thus, the measure of the complementary angle is
.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Extra Insights
The measure of a complementary angle is found by subtracting the given angle from
. So, for an angle measuring
, you would do the following calculation:
. Therefore, the complementary angle measures
.
Did you know that the concept of complementary angles has been around since the ancient Greeks? They studied geometry extensively and laid the groundwork for many mathematical principles we still use today. Complementary angles are often visually represented in right triangles, showing how angles work together!
In practical applications, understanding complementary angles can be crucial in fields like architecture and engineering. For instance, when designing a roof, knowing how to calculate the complementary angles can help ensure proper drainage. So next time you see a triangle or a roof, remember the angles are working together to keep everything in harmony!