Answer:
(2) 42°
Explanation:
Copy of the given problem:
4. Multiple-Choice
1. Two complementary angles measure (12r - 18)° and (5x + 23)°. What
is the measure of the smaller angle?
(1) 5°
(2) 42°
(3) 48°
(4) 90°
Solution:
The sum of the measures of complementary angles is 90 deg.
12r - 18 + 5x + 23 = 90
We have 1 equation with two different variables, so we cannot solve the equation to find unique values of the variables.
I assume the above is an error, and both variables should be the same.
12r - 18 + 5r + 23 = 90
Combine like terms on the left side. Terms with r are combined. Terms with no variable are combined.
12r + 5r - 18 + 23 = 90
17r + 5 = 90
Subtract 5 from both sides.
17r = 85
Divide both sides by 5.
r = 5
The measures of the angles are:
12r - 18 = 12(5) - 18 = 60 - 18 = 42
5r + 23 = 5(5) + 23 = 25 + 23 = 48
The measures of the two angles are 42° and 48°.
The smaller angle measures 42°
Answer: (2) 42°