Measuring Angles

Measuring AnglesGeometryMrs. King

Unit 1, Lesson 5

Definition

Angle: formed by two rays with a common endpoint (“vertex”).

C

A

B

Name the angle below in four ways.

*The name can be the vertex of the angle: G.

The name can be a point on one side, the vertex, and a point on the other side of the angle: AGC, CGA.

The name can be the number inside of the angle: 3.

Practice

Types of Angles

1. AcuteLess than 90°

2. RightExactly 90°

3. ObtuseGreater than 90°,

but less than 180°

Types of Angles

4. StraightExactly 180°

5. ReflexGreater than

180 but less than 360

Definition

Congruent Angles: angles with the same measure

Angle Addition Postulate

1-8: If point B is in the interior of AOC, then mAOB + mBOC = mAOC

O C

BA

PracticemHAT = 50 and mHAM = 125. What is the mMAT?

A H

TM

m 1 + m 2 = m ABC

42 + m 2 = 88

m 2 = 46

Suppose that m 1 = 42 and m ABC = 88. Find m 2.

Practice

Angle Pairs

1. Vertical Angles: two angles whose sides are opposite rays

1 and 3 are vertical angles, and 2 and 4 are vertical angles.

2. Adjacent Angles: two coplanar angles with a common side, a common vertex, and no common interior points.

1 and 2 are adjacent angles

Angle Pairs

3. Complementary Angles: two angles whose measures have a sum of 90.

4. Supplementary Angles: Two angles whose measures have a sum of 180.

In the diagram, these angles are supplementary:1 and 2,

2 and 3,

3 and 4,

and 4 and 1.

Homework

Measuring Angles in Student Practice Packet(Page 6, #1-13)