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Objective

Identify and apply angle relationships

Vocabulary

Vertical angles

Opposite angles formed by the intersection of two lines

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Vocabulary

Congruent angles

Angles that have the same measure

Vocabulary

Supplementary angles

Two angles that have the sum of their measures as 1800

Vocabulary

Complementary angles

Two angles are complementary if the sum of their measures is 900

Math Symbols

Is congruent to

Example 1 Classify Angles

Example 2 Classify Angles

Example 3 Find a Missing Angle Measure

Example 4 Use Angles to Solve A Problem

Classify the pair of angles as complementary, supplementary, or neither

Answer:.

Add the two angle measurements together

1800

Supplementary

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1280 + 520

Meets the definition of supplementary angles

Answer: complementary

Classify the pair of angles as complementary, supplementary, or neither

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Classify the pair of angles as complementary, supplementary, or neither

x and y form a right angle

Complementary

Right angle = 900

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Meets the definition of complementary anglesAnswer:

Answer: supplementary

Classify the pair of angles as complementary, supplementary, or neither

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Angles PQS and RQS are supplementary.If mPQS 56, find mRQS.

560

PQS and RQS are supplementary

Remember: Supplementary angles = 1800

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mPQS is 560

mPQS + mRQS = 1800

Angles PQS and RQS are supplementary.If mPQS 56, find mRQS.

560

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Replace mPQS with 560

mPQS + mRQS = 1800

560

Bring down + mRQS = 1800

+ mRQS = 1800

Solve for the unknown mRQS

Angles PQS and RQS are supplementary.If mPQS 56, find mRQS.

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Ask “what is being done to the variable?”mPQS + mRQS = 1800

560 + mRQS = 1800 The variable (mRQS) is being added by 560

Do the inverse on both sides of the equal sign

Bring down 560

560

Subtract 560

- 560

Angles PQS and RQS are supplementary.If mPQS 56, find mRQS.

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mPQS + mRQS = 1800

560 + mRQS = 1800

Bring down + mRQS = 1800

560

Subtract 560

- 560 - 560 + mRQS = 1800 Combine “like” terms00 Bring down + mRQS =

Combine “like” terms

+ mRQS = 1240

Angles PQS and RQS are supplementary.If mPQS 56, find mRQS.

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mPQS + mRQS = 1800

560 + mRQS = 1800

Use the Identify Property to add 00 + mRQS

560 - 560 - 560 + mRQS = 1800

00 + mRQS = 1240

mRQS = 1240 Answer:

Bring down 1240

Angles MNP and KNP are complementary. If mMNP 23, find mKNP.

Answer: m KNP = 67

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GEOMETRY The rectangle shown is divided by a diagonal. Find the value of x.

The angle that x0 and 700 make is a right angle

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A right angle = 900

Write an equation

x0 + 700 = 900

Solve for the unknown

GEOMETRY The rectangle shown is divided by a diagonal. Find the value of x.

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x0 + 700 = 900 Ask “what is being done to the variable?”

The variable is being added by 700

Do the inverse on both sides of the equal sign

Bring down x0 + 700

X0 + 700

Subtract 700

- 700

GEOMETRY The rectangle shown is divided by a diagonal. Find the value of x.

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x0 + 700 = 900 Bring down = 900

x0 + 700

Subtract 700 - 700 = 900 - 700

Combine “like” terms

Bring down x0 +

x0 + 00

Bring down = =

Combine “like” terms

200

Use the Identify Property to add x + 00

x0 = 200

Answer:

Bring down 200

GRAPHING In the circle graph shown below, find the value of x.

Answer: x = 620

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Assignment Lesson 10:3 Angle Relationship 3 - 21 All