WARM UP Find the complement of where An

WARM UP Find the complement of , where An angle measures 6 more than 3 times its supplement. Find the measure of its supplement.

SPECIAL ANGLE PAIRS

Complimentary Angles that sum to 90°

Supplementary Angles that sum to 180°

Not all intersecting lines form right angles, but they do form four angles that have special relationships. V X Z Y W

Adjacent To be next to. SHARING a side.

Vertical Angles Two non-adjacent angles formed by two intersecting lines. Angles that are ACROSS from each other when two lines cross.

Vertical Angles V X Z Y W Vertical angles are ALWAYS CONGRUENT

Linear Pair Adjacent angles whose noncommon sides are opposite rays. Two adjacent angles that are supplementary.

Linear Pair V X Z Y W m YZV + m VZX = 180°

Example 1 AC and DE intersect at B. Find the value of ‘x’ and the measure of EBC. A (2 x + 20) E B (3 x + 15) D C

Example 2 GH and JK intersect at I. Find the value of ‘x’ and the measure of JIH. G (16 x – 20) K J I (13 x + 7) H

Example 3 LN and OP intersect at M. Find the value of ‘x’ and the measures of LMO and OMN. O (5 x + 10) N (7 x + 20) L P M

Example 4 If 1 and 2 are complements, with m 1 = (2 x + 20) and m 2 = (3 x + 15) , find the value of ‘x’.

Example 5 Find all of the missing angles. m 1 = _____ m 2 = _____ m 3 = _____ m 4 = _____ 4 110 45 1 3 2

Example 6 CD AB, m 1 = (6 x – 3) , m 2 = (7 x – 11). Find the value of ‘x’. A 2 C B 1 D