Holt McDougal Geometry 1-4 Pairs of Angles Simplify each expression – (x + 20) – (3x – 10) Write an algebraic expression for each of the following more than twice a number 4. 6 less than half a number 70 – x 190 – 3x 2n + 4 Flashback

Holt McDougal Geometry 1-4 Pairs of Angles Identify adjacent, vertical, complementary, and supplementary angles. Find measures of pairs of angles. GOALS!

Holt McDougal Geometry 1-4 Pairs of Angles Draw an example of adjacent angles. Draw an example of a linear pair.

Holt McDougal Geometry 1-4 Pairs of Angles Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. Example 1: Identifying Angle Pairs AEB and BED Adjacent and form a linear pair

Holt McDougal Geometry 1-4 Pairs of Angles Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. Example 2: Identifying Angle Pairs AEB and BEC Only adjacent

Holt McDougal Geometry 1-4 Pairs of Angles DEC and AEB Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. Example 3: Identifying Angle Pairs Not Adjacent

Holt McDougal Geometry 1-4 Pairs of Angles 5 and 6 Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. Adjacent and form a linear pair

Holt McDougal Geometry 1-4 Pairs of Angles 7 and SPU Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. Not adjacent

Holt McDougal Geometry 1-4 Pairs of Angles 7 and 8 Tell whether the angles are only adjacent, adjacent and form a linear pair, or not adjacent. Not adjacent

Holt McDougal Geometry 1-4 Pairs of Angles Complementary angles- What is the complement of 30 ⁰ ? What is the complement of 44.2 ⁰ ?

Holt McDougal Geometry 1-4 Pairs of Angles Complementary angles- What is the complement of 30 ⁰ ? What is the complement of 44.2 ⁰ ? What is the complement of

Holt McDougal Geometry 1-4 Pairs of Angles Supplementary angles- What is the supplement of 30 ⁰ ? What is the supplement of 44.2 ⁰ ? What is the supplement of

Holt McDougal Geometry 1-4 Pairs of Angles Warm Up 1.) Find the complement of an angle that measures 30°. 2.) Find the supplement of an angle that measures 100°.

Holt McDougal Geometry 1-4 Pairs of Angles Find the measure of each of the following. Example 4: Finding the Measures of Complements and Supplements A. complement of F B. supplement of G 90 – 59 = 31 (180 – x) 180 – (7x+10) = 180 – 7x – 10 = (170 – 7x) (90 – x)

Holt McDougal Geometry 1-4 Pairs of Angles a. complement of E Find the measure of each of the following. b. supplement of F = (102 – 7x)° 180 – 116.5° = 90° – (7x – 12)° = 90° – 7x° + 12° (90 – x)° (180 – x)

Holt McDougal Geometry 1-4 Pairs of Angles Find the measure of each of the following. Example 3: Using complements and supplements A. Find the value of b. B. Find the value of x b = 27 x + 18 = 180 X = b = 90

Holt McDougal Geometry 1-4 Pairs of Angles Example 6 ∠ R and ∠ S are complementary. If m ∠ R = 7 + 3x and m ∠ S = 2x What is the value of x. Find the measure of both angles x + 2x + 13 = 90 x = 14 Set up the equation! Solve for x! R = 49 and 41

Holt McDougal Geometry 1-4 Pairs of Angles ∠ DEF and ∠ FEG are supplementary. m ∠ DEF = 9x + 1 and m ∠ FEG = 8x + 9. Find the measure of both angles. x = 10 ∠ DEF = 91 and ∠ FEG =89

Holt McDougal Geometry 1-4 Pairs of Angles Light passing through a fiber optic cable reflects off the walls of the cable in such a way that 1 ≅ 2, 1 and 3 are complementary, and 2 and 4 are complementary. If m1 = 47°, find m2, m3, and m4. Example 7: Problem-Solving Application m2 = 47°, m3 = 43°, and m4 =43°.

Holt McDougal Geometry 1-4 Pairs of Angles What if...? Suppose m3 = 27.6°. Find m1, m2, and m4. Thus m1 = m2 = 62.4°; m4 = 27.6°.

Holt McDougal Geometry 1-4 Pairs of Angles Assignment: Page ,26-31

Holt McDougal Geometry 1-4 Pairs of Angles Warm up The measurement of angle A is 64.1° and the measurement of angle B is (4x – 30)°. 1.) Find the supplement of angle A. 2.) Find the complement of angle B.

Holt McDougal Geometry 1-4 Pairs of Angles Day 2 Vertical Angles

Holt McDougal Geometry 1-4 Pairs of Angles

Holt McDougal Geometry 1-4 Pairs of Angles Vertical angles A and C are vertical angles, as are B and D. Name two sets of vertical angles What do you know about ∠ A and ∠ C? What do you know about ∠ B and ∠ D?

Holt McDougal Geometry 1-4 Pairs of Angles Lesson Quiz: Part I mA = 64.1°, and mB =(4x – 30)°. Find the measure of each of the following. 1. supplement of A 2. complement of B 3. Determine whether this statement is true or false. If false, explain why. If two angles are complementary and congruent, then the measure of each is 90°. (120 – 4x) ° 115.9° False; each is 45°.

Holt McDougal Geometry 1-4 Pairs of Angles Lesson Quiz: Part II mXYZ = 2x° and mPQR = (8x - 20)°. 4. If XYZ and PQR are supplementary, find the measure of each angle. 5. If XYZ and PQR are complementary, find the measure of each angle. 22°; 68° 40°; 140°

Holt McDougal Geometry 1-4 Pairs of Angles Warm Up The measurement of angle XYZ = 2x° and the measurement of angle PQR = (8x – 20)°. 1.)If XYZ and PQR are supplementary find the measure of each angle. 2.) If XYZ and PQR are complementary, find the measure of each angle.