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CCSS

Content StandardsPreparation for G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. Mathematical Practices2 Reason abstractly and quantitatively. 3 Construct viable arguments and critique the reasoning of others.

Then/Now

You measured and classified angles.

• Identify and use special pairs of angles.

• Identify perpendicular lines.

Vocabulary

• adjacent angles

• linear pair

• vertical angles

• complementary angles

• supplementary angles

• perpendicular

Vocabulary

• Adjacent angles:

two angles that lie in the same plane and have a common vertex and a common

side

Vocabulary

• Linear pair:

a pair of adjacent angles with noncommon sides that are opposite rays for a total measure of 180°

Vocabulary

• Vertical angles:

two nonadjacent angles formed by two intersecting lines that have equal measure

Vocabulary

• Complementary angles:

two angles with measures that have a sum of 90°

Vocabulary

• Supplementary angles:

two angles with measures that have a sum of 180°

Vocabulary

• Perpendicular:

lines, segments, or rays that form right angles

Concept

Identify Angle Pairs

A. ROADWAYS Name an angle pair that satisfies the condition two angles that form a linear pair.

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

Identify Angle Pairs

B. ROADWAYS Name an angle pair that satisfies the condition two acute vertical angles.

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

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.

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.

Angle Measure

6x – 6 = 180 Simplify.

6x = 186 Add 6 to each side.

x = 31 Divide each side by 6.

Solve

Angle Measure

Use the value of x to find each angle measure.

mA = x mB = 5x – 6 = 31 = 5(31) – 6 or 149

Answer: mA = 31, mB = 149

Check Add the angle measures to verify that the angles are supplementary. mA + mB = 180

31 + 149 = 180180 = 180

ALGEBRA Find the measures of two complementary angles if one angle measures six degrees less than five times the measure of the other.

A. 1°, 1°

B. 21°, 111°

C. 16°, 74°

D. 14°, 76°

ALGEBRA Find the measures of two complementary angles if one angle measures six degrees less than five times the measure of the other.

Concept

Concept

Perpendicular Lines

ALGEBRA Find x and y so thatKO and HM are perpendicular.

Interpret Figures

A. Determine whether the following statement can be justified from the figure below. Explain.mVYT = 90

Interpret Figures

A. Determine whether the following statement can be justified from the figure below. Explain.mVYT = 90

Interpret Figures

B. Determine whether the following statement can be justified from the figure below. Explain.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.

Interpret Figures

C. Determine whether the following statement can be justified from the figure below. Explain.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.