Answer:
1. B; the measure of the smaller angle is 35°
2. A; the value of x is 20
3. B; the measure of the larger angle is 52°
Step-by-step explanation:
1. We see that these two angles add up to 90 degrees, so:
x + (x - 20) = 90
2x - 20 = 90
2x = 110
x = 110/2 = 55
The two angles are thus 55 and 55 - 20 = 35. So, B is wrong; it should be "the measure of the smaller angle is 35°".
2. These two angles are on a line so they add up to 180 degrees:
3x + 6x = 180
9x = 180
x = 180/9 = 20
So the angle measures are 3 * 20 = 60 and 6 * 20 = 120. Then A is wrong; it should be "the value of x is 20".
3. Since the angles are complementary, they add up to 90. Then:
2x + (3x - 5) = 90
5x - 5 = 90
5x = 95
x = 95/5 = 19
So the two angles are 2 * 19 = 38 and 3 * 19 - 5 = 52. So B is wrong; it should be "the measure of the larger angle is 52°".
