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Geometry Angles and Theorems: Understanding Angle Relationships

Learn to identify and solve angles using Corresponding Angles Postulate and Vertical Angles Congruence Theorem. Practice with guided examples to master concepts.

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Geometry Angles and Theorems: Understanding Angle Relationships

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  1. The measure of three of the numbered angles is 120°. Identify the angles. Explain your reasoning. By the Corresponding Angles Postulate, m5=120°. Using the Vertical Angles Congruence Theorem, m4=120°. Because 4 and 8 are corresponding angles, by the Corresponding Angles Postulate, you know that m8 = 120°. EXAMPLE 1 Identify congruent angles SOLUTION

  2. ALGEBRA Find the value of x. By the Vertical Angles Congruence Theorem, m4=115°. Lines aand bare parallel, so you can use the theorems about parallel lines. m4 + (x+5)° 180° = 115° + (x+5)° 180° = Substitute 115° for m4. x + 120 = 180 x = 60 EXAMPLE 2 Use properties of parallel lines SOLUTION Consecutive Interior Angles Theorem Combine like terms. Subtract 120 from each side.

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

  4. Use the diagram. 2. If m 3 = 68° and m 8 = (2x + 4)°, what is the value of x? Show your steps. 180 m 7 + m 8 = m 7 ANSWER 68 + 2x + 4 = 180 2x + 72 = 180 m 3 = 2x = 108 x = 54 for Examples 1 and 2 GUIDED PRACTICE

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