Find the complement of , where

Find the complement of , where )103( xT

WARM UP

T

An angle measures 6 more than 3 times its supplement. Find the measure of its supplement.

ComplimentaryComplimentaryAnglesAngles

Angles that sum to 90°

SupplementarySupplementaryAnglesAngles

Angles that sum to 180°

Not all intersecting lines form right angles, but they do form four angles that have special relationships.

V

Z

WY

X

AdjacentAdjacent

To be next to.

SHARING a side.

Vertical AnglesVertical AnglesTwo non-adjacent angles formed

by two intersecting lines.

Angles that are ACROSS from each other when

two lines cross.

Vertical AnglesVertical AnglesV

Z

WY

X

Vertical angles are ALWAYS CONGRUENT

Linear PairLinear PairAdjacent angles whose non-

common sides are opposite rays.

Two adjacent angles that are supplementary.

Linear PairLinear Pair

V

Z

WY

X

mYZV + mVZX = 180°

Example 1

AC and DE intersect at B. Find the value of ‘x’ and the measure of EBC.

A

B

CD

E(2x + 20)

(3x + 15)

Example 2

GH and JK intersect at I. Find the value of ‘x’ and the measure of JIH.

G

I

H

K

J(16x – 20)

(13x + 7)

Example 3

LN and OP intersect at M. Find the value of ‘x’ and the measures of LMO and OMN.

L

M

NO

P

(7x + 20)

(5x + 10)

Example 4

If 1 and 2 are complements, with m1 = (2x + 20) and m2 = (3x + 15), find the value of ‘x’.

Example 5

Find all of the missing angles.

m1 = __________m2 = __________m3 = __________m 4 = __________

12

3

4110

45

Example 6

CD AB, m1 = (6x – 3), m2 = (7x – 11). Find the value of ‘x’.

A

B

D

21

C