Portal:Euclidean geometry/Chapter 13
Introduction
[edit | edit source]An angle is the intersection of two rays at a common endpoint. Angles are normally measured in degrees. There are four types of angles:
- Acute: any angle measuring less than 90 degrees but more than 0 degrees
- Right: any angle measuring 90 degrees
- Obtuse: any angle measuring more than 90 degrees but less than 180 degrees
- Straight: any angle that measures either 0 or 180 degrees (these two measurements mean basically the same thing)
Complementary Angles
[edit | edit source]The Concept
[edit | edit source]Complementary angles add up to 90 degrees.
Why it Matters
[edit | edit source]If you know two angles are complementary, you can find the measure of the second by subtracting the first from 90.
EXAMPLE 1: Two angles add up to 90 degrees. One angle measures 36 degrees. What is the measure of the other angle? SOLUTION: As we know the angles add up to 90 degrees, the problem becomes simple subtraction: 90-36=54 ANSWER: 54 degrees
Supplementary Angles
[edit | edit source]The Concept
[edit | edit source]Supplementary angles add up to 180 degrees.
Why it Matters
[edit | edit source]If you know two angles are supplementary, you can find the measure of the second by subtracting the first from 180.
EXAMPLE 2: Two angles add up to 180 degrees. One angle measures 26 degrees. What is the measure of the other angle? SOLUTION: Like in Example 1, we know what the angles add up to. The problem, yet again, becomes simple subtraction: 180-26=154 ANSWER: 154 degrees
Vertical Angles
[edit | edit source]The Concept
[edit | edit source]Vertical angles are angles created by the intersection of two lines. Angles on different sides of both of these lines are vertical angles, and angles on the same side of both of these lines are supplementary.
Why it Matters
[edit | edit source]If we know two angles are vertical angles, we know the angles are equal.