EXAMPLE 1 Identify congruent angles SOLUTION By the Corresponding Angles Postulate, m 5 = 120°. Using the Vertical Angles Congruence Theorem, m 4 = 120°.

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Presentation transcript:

EXAMPLE 1 Identify congruent angles SOLUTION By the Corresponding Angles Postulate, m 5 = 120°. Using the Vertical Angles Congruence Theorem, m 4 = 120°. Because 4 and 8 are corresponding angles, by the Corresponding Angles Postulate, you know that m 8 = 120°. The measure of three of the numbered angles is 120°. Identify the angles. Explain your reasoning.

EXAMPLE 2 Use properties of parallel lines ALGEBRA Find the value of x. SOLUTION By the Vertical Angles Congruence Theorem, m 4 = 115°. Lines a and b are parallel, so you can use the theorems about parallel lines. Consecutive Interior Angles Theorem m 4 + (x+5)° = 180° Substitute 115° for m ° + (x+5)° = 180° Combine like terms. x = 180 Subtract 120 from each side. x = 60

GUIDED PRACTICE for Examples 1 and 2 SOLUTION Vertical Angles Congruence Theorem. m 4 = 105° Corresponding Angles Postulate. m 5 =105° Alternate Exterior Angles Theorem m 8 =105° Use the diagram at the right. 1. If m 1 = 105°, find m 4, m 5, and m 8. Tell which postulate or theorem you use in each case.

GUIDED PRACTICE for Examples 1 and 2 Use the diagram at the right. 2. If m 3 = 68° and m 8 = (2x + 4)°, what is the value of x ? Show your steps.

GUIDED PRACTICE for Examples 1 and 2 SOLUTION 7 and 5 are supplementary. m 7 + m 8 = 180° Corresponding Angles Postulate. m 3 =m 7 m 3 =68° Substitute 68° for m 7 and (2x + 4) for 8. 68° + 2x + 4 =180° Combine like terms x =180° Subtract 72 from each side. 2x =108 Divide each side by 2. x =54

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