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Concept

Learn to identify and calculate various angle pairs, including linear pairs, vertical angles, and supplementary angles in geometry. Includes sample problems and solutions.

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Concept

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  1. Concept

  2. 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

  3. 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

  4. Concept

  5. 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. UnderstandThe 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

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

  7. Angle Measure 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

  8. Concept

  9. ALGEBRA Find x and y so thatKO and HM are perpendicular. Perpendicular Lines Example 3

  10. 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

  11. 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

  12. Concept

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

  14. 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

  15. 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

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

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