Question

two angles are complementary. the smaller angle is 47 degrees less than the larger angle. what is the measurement of the smaller angle? be precise in the measurement, including any decimal value. you only need to enter the value for the angle. no other symbols or unit information needed.

Explanation:

Step1: Let the larger angle be \( x \) degrees.

Then the smaller angle is \( x - 47 \) degrees.

Step2: Use the property of complementary angles.

Since the two angles are complementary, \( x+(x - 47)=90 \).
Simplify the equation: \( 2x-47 = 90 \).
Add 47 to both sides: \( 2x=90 + 47=137 \).
Divide both sides by 2: \( x=\frac{137}{2}=68.5 \).

Step3: Find the measure of the smaller angle.

Substitute \( x = 68.5 \) into \( x - 47 \).
The smaller angle is \( 68.5-47 = 21.5 \).

Answer:

21.5