Answer:
17. 33 and 57
18. 49 and 41
19. 30 and 60
20. 80 and 10
21. 30 and 150
22. 20 and 160
23. 108 and 72
Explanation:
Complementary angles are two angles whose measures have a sum of 90 degrees. In each case, let one unknown measure be x. Then, the other unknown measure is related to x the way the problem tells you. Then add the measures and set equal to 90. Solve for x. Finally, find the measure of the other angle.
17. One angle measures x. The measure of the other angle is 24 degrees greater, so it is x + 24. Now add the measures and set equal to 90.
x + x + 24 = 90
2x + 24 = 90
2x = 66
x = 33
x + 24 = 33 + 24 = 57
The measures are 33 and 57.
18. One angle measures x. The other angle measures 8 less than x, so it measures x - 8.
x + x - 8 = 90
2x - 8 = 90
2x = 98
x = 49
x - 8 = 49 - 8 = 41
The measures are 49 and 41.
19. One angle measures x. The measure of the other angle is 30 degrees greater, so it is x + 30. Now add the measures and set equal to 90.
x + x + 30 = 90
2x + 30 = 90
2x = 60
x = 30
x + 30 = 30 + 30 = 60
The measures are 30 and 60.
20. One angle measures x. The other angle measures 70 less than x, so it measures x - 70.
x + x - 70 = 90
2x - 70 = 90
2x = 160
x = 80
x - 70 = 80 - 70 = 10
The measures are 80 and 10.
Supplementary angles are two angles whose measures have a sum of 180 degrees.
21. One angle measures x. The measure of the other angle is 5 times the measure of the first angle, so it is 5x.
x + 5x = 180
6x = 180
x = 30
5x = 5(30) = 150
The angles measure 30 and 150.
22. One angle measures x. The measure of the other angle is 8 times the measure of the first angle, so it is 8x.
x + 8x = 180
9x = 180
x = 20
8x = 8(20) = 160
The angles measure 20 and 160.
23. One angle measures x. The measure of the other angle is 2/3 the measure of the first angle, so it is (2/3)x.
x + (2/3)x = 180
(3/3)x + (2/3)x = 180
(5/3)x = 180
3/5 * (5/3)x = 3/5 * 180
x = 108
(2/3)x = 2/3 * 108 = 72
The angles measure 108 and 72.