Concept

Sample Answers: ∠PIQ and ∠QIS, ∠PIT and ∠TIS, ∠QIU and ∠UIT Identify Angle Pairs A. ROADWAYS Name an angle pair that satisfies the condition two angles that form a linear pair. A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays. Sample Answers: ∠PIQ and ∠QIS, ∠PIT and ∠TIS, ∠QIU and ∠UIT Example 1

Sample Answers: ∠PIU and ∠RIS, ∠PIQ and ∠TIS, ∠QIR and ∠TIU Identify Angle Pairs B. ROADWAYS Name an angle pair that satisfies the condition two acute vertical angles. Sample Answers: ∠PIU and ∠RIS, ∠PIQ and ∠TIS, ∠QIR and ∠TIU Example 1

Concept

Plan Draw two figures to represent the angles. Angle Measure ALGEBRA Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the measure of the other angle. Understand The problem relates the measures of two supplementary angles. You know that the sum of the measures of supplementary angles is 180. Plan Draw two figures to represent the angles. Example 2

Solve 6x – 6 = 180 Simplify. 6x = 186 Add 6 to each side. Angle Measure Solve 6x – 6 = 180 Simplify. 6x = 186 Add 6 to each side. x = 31 Divide each side by 6. Example 2

Use the value of x to find each angle measure. m∠A = x m∠B = 5x – 6 = 31 = 5(31) – 6 or 149 Check Add the angle measures to verify that the angles are supplementary. m∠A + m∠B = 180 31 + 149 = 180 180 = 180 ✓ Answer: m∠A = 31, m∠B = 149 Example 2

Concept

ALGEBRA Find x and y so that KO and HM are perpendicular. Perpendicular Lines ALGEBRA Find x and y so that KO and HM are perpendicular. Example 3

84 = 12x Subtract 6 from each side. 7 = x Divide each side by 12. Perpendicular Lines 90 = (3x + 6) + 9x Substitution 90 = 12x + 6 Combine like terms. 84 = 12x Subtract 6 from each side. 7 = x Divide each side by 12. Example 3

84 = 3y Subtract 6 from each side. 28 = y Divide each side by 3. Perpendicular Lines To find y, use m∠MJO. m∠MJO = 3y + 6 Given 90 = 3y + 6 Substitution 84 = 3y Subtract 6 from each side. 28 = y Divide each side by 3. Answer: x = 7 and y = 28 Example 3

Concept

Interpret Figures A. Determine whether the following statement can be justified from the figure below. Explain. m∠VYT = 90 Example 4

∠TYW and ∠TYU are supplementary. Interpret Figures B. Determine whether the following statement can be justified from the figure below. Explain. ∠TYW and ∠TYU are supplementary. Answer: Yes, they form a linear pair of angles. Example 4

∠VYW and ∠TYS are adjacent angles. Interpret Figures C. Determine whether the following statement can be justified from the figure below. Explain. ∠VYW and ∠TYS are adjacent angles. Answer: No, they do not share a common side. Example 4

Think, Write, Pair, Share A. Determine whether the statement m∠XAY = 90 can be assumed from the figure. A. yes B. no Example 4a