Portal:Euclidean geometry/Chapter 13

Introduction

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

The Concept

Complementary angles add up to 90 degrees.

Why it Matters

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

The Concept

Supplementary angles add up to 180 degrees.

Why it Matters

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

The Concept

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

If we know two angles are vertical angles, we know the angles are equal.