While watching the pitcher warm up, Phillip thinks, “I’ll

25. Given:

m ⬔3 = 7x - 21 m ⬔4 = 3x + 7 Find: m ⬔FMH

26. Given:

m ⬔FMH = 4x + 1 m ⬔4 = x + 4 Find: m ⬔4

27. In the figure, find:

a 傽 b 傼 c ⬔KMJ 傽 ⬔JMH d 傼

28. Given:

⬔EFG is a right angle m ⬔HFG = 2x - 6 m ⬔EFH = Find: m ⬔EFH

29. Two angles are supplementary. One angle is 40° more

than four times the other. Find the measures of the two angles.

30. a Write an expression for the perimeter of the triangle

shown. HINT: Add the lengths of the sides. b If the perimeter is 32 centimeters, find the value of x. c Find the length of each side of the triangle. 3 m ⬔HFG MH MK MH MJ Í FJ Í KH

38. Fill in the missing statements or reasons.

Given: ⬔1 ⬵ ⬔P ⬔4 ⬵ ⬔P bisects ⬔RVO Prove: ⬔TVP ⬵ ⬔MVP VP K H 4 3 M J F Exercises 25–27 x + 7 3x – 2 2x + 3 1 2 3

31. The sum of the measures of all three angles of the tri-

angle in Review Exercise 30 is 180°. If the sum of the measures of angles 1 and 2 is more than 130°, what can you conclude about the measure of angle 3?

32. Susan wants to have a 4-ft board with some pegs on it.

She wants to leave 6 in. on each end and 4 in. between pegs. How many pegs will fit on the board? HINT: If n represents the number of pegs, then n - 1 represents the number of equal spaces. State whether the sentences in Review Exercises 33 to 37 are always true A, sometimes true S, or never true N.

33. If AM

= MB , then A, M, and B are collinear. 34. If two angles are congruent, then they are right angles. 35. The bisectors of vertical angles are opposite rays.

36. Complementary angles are congruent. 37. The supplement of an obtuse angle is another obtuse

angle.

3 4

1 2 T M O P R V PROOF Statements Reasons 1. ⬔1 ⬵ ⬔P 1. Given 2. ? 2. Given 1, 2 3. ? 3. Transitive Prop. of ⬵ 3 4. m ⬔1 = m ⬔4 4. ? 5. bisects ⬔RVO 5. ? 6. ? 6. If a ray bisects an ⬔, it forms two ⬔s of equal measure 4, 6 7. ? 7. Addition Prop. of Equality 8. m ⬔1 + m ⬔2 = 8. ? m ⬔TVP; m ⬔4 + m ⬔3 = m ⬔MVP 7, 8 9. m ⬔TVP = 9. ? m ⬔MVP 10. ? 10. If two ⬔s are = in measure, then they are ⬵ Write two-column proofs for Review Exercises 39 to 46. VP K J F H G Exercises 39–41

39. Given: ⊥

⬔JHF is a right ⬔ Prove: ⬔KFH ⬵ ⬔JHF FH KF G F H E