⬔FAC and ⬔CAD are adjacent and

18. Given:

m ⬔RST = 2x + 9 m ⬔TSV = 3x - 2 m ⬔RSV = 67° Find: x

19. Given:

m ⬔RST = 2x - 10 m ⬔TSV = x + 6 m ⬔RSV = 4x - 6 Find: x and m ⬔RSV

20. Given:

m ⬔RST = 5x + 1 - 3 m ⬔TSV = 4x - 2 + 3 m ⬔RSV = 42x + 3 - 7 Find: x and m ⬔RSV

21. Given:

m ⬔RST = m ⬔TSV = m ⬔RSV = 45° Find: x and m ⬔RST

22. Given: m

⬔RST = m ⬔TSV = m ⬔RSV = 49° Find: x and m ⬔TSV

23. Given:

bisects ⬔RSV m ⬔RST = x + y m ⬔TSV = 2x - 2y m ⬔RSV = 64° Find: x and y

24. Given:

bisects ⬔RSV Find: x and y

25. Given:

and in plane P as shown; intersects P at point A ⬔CAB ⬵ ⬔DAC ⬔DAC ⬵ ⬔DAB What can you conclude? Í AD Í AC Í AB m ⬔RSV = 80° m ⬔TSV = 3x - y + 2 m ⬔RST = 2x + 3y ST ST x 2 2x 3 x 4 x 2 R S T V Exercises 16–24 D C A P B

26. Two angles are complementary. One angle is 12° larger

than the other. Using two variables x and y, find the size of each angle by solving a system of equations.

27. Two angles are supplementary. One angle is 24° more

than twice the other. Using two variables x and y, find the measure of each angle.

28. For two complementary angles, find an expression for the

measure of the second angle if the measure of the first is: a x° b 3x - 12° c 2x + 5y°

29. Suppose that two angles are supplementary. Find

expressions for the supplements, using the expressions provided in Exercise 28, parts a to c.

30. On the protractor shown, bisects

⬔MNQ. Find x. NP x 53 ° 92° M N P Q Exercises 30, 31

31. On the protractor shown for Exercise 30,

⬔MNP and ⬔PNQ are complementary. Find x.

32. Classify as true or false:

a If points P and Q lie in the interior of ⬔ABC, then lies in the interior of ⬔ABC. b If points P and Q lie in the interior of ⬔ABC, then lies in the interior of ⬔ABC. c If points P and Q lie in the interior of ⬔ABC, then lies in the interior of ⬔ABC. In Exercises 33 to 40, use only a compass and a straightedge to perform the indicated constructions. PQ Í PQ PQ M R P Exercises 33–35

33. Given: Obtuse

⬔MRP Construct: With as one side, an angle ⬵ ⬔MRP

34. Given: Obtuse

⬔MRP Construct: , the angle bisector of ⬔MRP

35. Given: Obtuse

⬔MRP Construct: Rays , , and so that ⬔MRP is RU RT RS RS OA D F E divided into four ⬵ angles

36. Given: Straight

⬔DEF Construct: A right angle with vertex at E HINT: Use Construction 4.