Define variables for the measures of angles. Write equations based on the given facts as well as the characteristics of complementary angles and supplementary angles. Solve the given resulting system of equations by elimination.
a) Two angles are complementary. The measure of one angle is $30 ^ { \circ }$ larger than that of the other.
b) Two angles are supplementary. The measure of one angle is $30 ^ { \circ }$ larger than that of the other.
A) a) $55,35$
b) $100,80$
B) a) $60,30$
b) $100,80$
C) a) $60,30$
b) $105,75$
D) a) $50,40$
b) $95,85$
E) a) $55,35$
b) $95,85$

Question

Define variables for the measures of angles. Write equations based on the given facts as well as the characteristics of complementary angles and supplementary angles. Solve the given resulting system of equations by elimination. 
a) Two angles are complementary. The measure of one angle is $30 ^ { \circ }$ larger than that of the other.
b) Two angles are supplementary. The measure of one angle is $30 ^ { \circ }$ larger than that of the other.
A) a) $55,35$
b) $100,80$
B) a) $60,30$
b) $100,80$
C) a) $60,30$
b) $105,75$
D) a) $50,40$
b) $95,85$
E) a) $55,35$
b) $95,85$

Quizplus · Accepted Answer

For a) in part A, we can let one angle be x, then the other angle is 30 degrees less, so it is x - 30. Since they are complementary, their sum is 90 degrees, so we have the equation x + x - 30 = 90. Solving for x, we get x = 60, which is one of the values listed in choice C.

For b) in part A, we can use the same approach but with the angles being supplementary instead of complementary. Let one angle be x, then the other angle is 30 degrees less, so it is x - 30. Since they are supplementary, their sum is 180 degrees, so we have the equation x + x - 30 = 180. Solving for x, we get x = 105, which is one of the values listed in choice C.

For part B, we can use the same approach as in part A, but with the angles being different values. In both cases, we can let one angle be x, then the other angle is 30 degrees less, so it is x - 30.

For a), since they are complementary, their sum is 90 degrees, so we have the equation x + x - 30 = 90. Solving for x, we get x = 60, which is one of the values listed in choice C.

For b), since they are supplementary, their sum is 180 degrees, so we have the equation x + x - 30 = 180. Solving for x, we get x = 105, which is one of the values listed in choice C.

Define Variables for the Measures of Angles 30∘30 ^ { \circ }30∘

Define Variables for the Measures of Angles $30 ^ { \circ }$