Final answer:
To find the measures of the two complementary angles given as (7x+17) and (3x-20), solve the equation that sets their sum equal to 90 degrees. Substituting the resulting x = 9.3 into the original expressions, the measures of the angles are found to be 82.1 degrees and 7.9 degrees.
Step-by-step explanation:
The question is about finding the measures of two angles which are complementary, given their algebraic expressions. In mathematical terms,the sum of complementary angles equals 90 degrees. So, by setting up an equation where (7x + 17) + (3x - 20) = 90, we can find the value of x and subsequently, the measures of the angles.
- Add the like terms on the left side of the equation: 10x - 3 = 90.
- Add 3 to both sides: 10x = 93.
- Divide by 10 to find the value of x: x = 9.3.
Substitute x = 9.3 into the original expressions to find the measures of the angles: The measure of the first angle = 7x+17 = 7*9.3+17 = 82.1 degrees. The measure of the second angle = 3x - 20 = 3*9.3 - 20 = 7.9 degrees.
Learn more about Complementary Angles