\fName two pairs of congruent angles in each figure. Justify your answers. 20. - A 21. 22. K M 23. Developing Proof Fill in the blanks to complete this proof of Theorem 2-5. If two angles are congruent and supplementary, then each is a right angle. Given: ZW and Z V are congruent and supplementary. Prove: ZW and Z V are right angles. LY Proof: ZW and Z V are congruent because a. ? . Because congruent angles have the same measure, m/W = b. ? . ZW and 2 V are supplementary because it is given. By the definition of supplementary angles, mZW+ mzV= c_! . Substituting m/ W for m_V. you get my W+ mz W = 180, or 2mZW = 180. By the d. ? Property of Equality, mZW = 90. Since mZW- mzV, mzV- 90 by the Transitive Property of Equality. Both angles are e. ? angles by the definition of right angles. 24. Design In the photograph, the legs of the table are constructed so that 21 = 22. What theorem can you use to justify the statement that 23 = 24? 25. Reasoning Explain why this statement is true: If mZABC + mZXYZ = 180 and ZABC = ZXYZ, then ZABC and Z XYZ are right angles. Algebra Find the measure of each angle. 26. ZA is twice as large as its complement, 2B. 27. LA is half as large as its complement, ZB. 28. ZA is twice as large as its supplement, Z B. 29. Z A is half as large as twice its supplement, Z B. 30. Write a proof for this form of Theorem 2-2. Proof If two angles are supplements of congruent angles, then the two angles are congruent. Given: &1 and Z2 are supplementary. 23 and 24 are supplementary. 42 = 24 Prove: 21 = 23 C Challenge 31. Coordinate Geometry LDOF contains points D(2, 3), O(0, 0), and A(5, 1). Find the coordinates of a point Fso that OF is a side of an angle that is adjacent and sunnlementary to / DOE