Solve the problem.
-Two angles are complementary if the sum of their measures is 90°. The measure of the first angle is 42° less than two times the second angle. Find the measure of each angle.
A)first angle = 51.6°
B)first angle = 63.6° second angle = 38.4° second angle = 26.4°
C)first angle = 26.4°
D)first angle = 38.4° second angle = 63.6° second angle = 51.6°

Question

Quizplus · Accepted Answer

Let x be the measure of the second angle. The first angle is 2x-42°. We know that the sum of these two angles is 90°, so we can set up the equation:
x + 2x-42° = 90°
Combining like terms:
3x-42° = 90°
Adding 42° to both sides:
3x = 132°
Dividing by 3:
x = 44°
Therefore, the second angle is 44°. 
To find the measure of the first angle, we use the equation: 
first angle = 2x-42 = 2(44)-42 = 46°
Therefore, the measures of the two angles are 46° and 44°. The answer is B. Let x be the second angle. Then the first angle is 2x - 42, since it is 42 less than twice the second angle. The sum of the two angles is x + (2x - 42) = 3x - 42, which is equal to 90° since the angles are complementary. Solving for x, we get x = 38.4°. Substituting this back into 2x - 42, we get the first angle to be 63.6°. Therefore, the answer is B, first angle = 63.6° and second angle = 38.4°.

Solve the Problem. -Two Angles Are Complementary If the Sum of Their Measures