A

Aim #1: How do we solve for unknown angles?

CC Geometry H

Do Now: Determine the measure of the missing angles in the diagrams below and

explain what facts about angles you used.

A.

B.

C.

360

`

x0

y0 1210

820

z0

1720

Two s AOC and COB with a common side OC, are _______________ s if C belongs to the interior of AOB.

The sum of angles on a straight line is 180? and two such s are called a linear pair. A linear pair of s are two adjacent s whose non-common sides form a straight line.

Two s are called supplementary if the sum of their measures is __________ two s are called complementary if the sum of their measures is __________. Describing s as supplementary or complementary refers only to the measures of their s the positions of the s or whether the pair of s is adjacent to each other is not part of the definition.

The total measure of the adjacent angles around a point is ________. The total measure of the adjacent angles on one side of a line is______.

Find mDCE:

B

Find mg:

A

E

720

C

D

Two s are vertical if their sides form opposite rays.

(RT and RU are opposite rays, RV and RS are opposite rays.) Vertical s have

_________ measure.

T

S

Find mTRV:

R

520

U V

Fill in the chart below using the diagrams given:

In the exercises below, AB, CD, and EF are line segments. Find the measure of each marked angle or find the value of the given variables. Give reasons for your calculations using the "Key Facts" handout. Show all the steps to your solutions. 1.

a = _____

2.

2.

b = _____

D C

C

B

E

F

y = ___________________

A

D

Let's sum it up!!! ? Adjacent angles are two angles with a common vertex and ray between them.

? Straight Angle: If two rays with the same vertex are distinct and collinear

(i.e. form a line), then each of the angles formed by the rays is called a straight . ? A straight angle measures 180o. ? Vertical Angles: Two angles are vertical angles (or vertically opposite angles) if their

sides form two pairs of opposite rays. ? Complementary angles are two angles with a sum of 90o. ? Supplementary angles are two angles with a sum of 180o.

? A linear pair of angles are adjacent and supplementary.

KEY FACTS

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