Answer:
21. <ABC = 58 Degrees
22. <LMN = 108 Degrees
23. <RSV = 42 Degrees
24. <LHK = 101 Degrees
28. <ABX = 112 Degrees and <CBX = 68 Degrees
29. <RSQ = 32 Degrees and <TSQ = 58 Degrees
30. <DEH = 39 Degrees and <FEH = 51 Degrees
Step-by-step explanation:
21. Add the degrees the find angle ABC
37 + 21 = 58
22. Add the degrees the find angle LMN
85 + 23 = 108
23. For this problem, you are suppose to subtract the angle measure given to you (72 degrees) from the degrees of the whole angle (<RST) to find the missing angle (RSV)
114 - 72 = 42
24. GHK is a straight line, meaning it equals 180 degrees. Subtract 180 from the angle measure given (79) to find the missing angle (LHK).
180 - 79 = 101
28. ABC is a straight line, meaning it equals 180 degrees. This also means that ABX + CBX = 180. First, find x, then use x to find the measures of ABX and CBX.
(14x + 70) + (20x + 8) = 180
Add Like Terms
34x + 78 = 180
Subtraction Prop. of Eq.
34x = 102
x = 3
Now, you can find the angle measures
14 * 3 + 70 = 112
20 * 3 + 8 = 68
(Make sure to check your work! 112 + 68 does indeed equal 180!)
29. RST is a right angle, meaning it equals 90 degrees. This also means that RSQ + TSQ = 90. First, find x, then use x to find the measures of RSQ and TSQ.
(15x - 43) + (8x + 18) = 90
Add Like Terms
23x - 25 = 90
Addition Prop of Eq.
23x = 115
x = 5
Now, you can find the angle measures
15 * 5 - 43 = 32
8 * 5 + 18 = 58
(Make sure to check your work! 32 + 58 does indeed equal 90!)
30. DEF is once again a right angle, so we follow the same steps from number 29.
13x + (10x + 21) = 90
Add Like Terms
23x + 21 = 90
Subtraction Prop of Eq.
23x = 69
x = 3
Now, you can find the angle measures
13 * 3 = 39
10 * 3 + 21 = 51
(Make sure to check your work! 39 + 51 does indeed equal 90!)
