Question

1. two angles are complementary. one angle is 8° more than the other. what are the measures of the two angles?

a. set up a system of two equations. let x represent the smaller angle and y represent the larger angle.
equation 1: ___
equation 2: ___
b. solve the system of equations by using the substitution method.

Explanation:

Step1: Define complementary - angle relationship

Since two angles are complementary, the sum of the two angles is 90 degrees. So, the first equation is $x + y=90$.

Step2: Define the size - relationship

One angle is 8 degrees more than the other. So, the second equation is $y=x + 8$.

Step3: Substitute and solve

Substitute $y=x + 8$ into $x + y=90$. We get $x+(x + 8)=90$. Expand the left - hand side: $2x+8 = 90$. Subtract 8 from both sides: $2x=90 - 8=82$. Divide both sides by 2: $x = 41$.

Step4: Find the value of y

Substitute $x = 41$ into $y=x + 8$. Then $y=41+8 = 49$.

Answer:

a. equation 1: $x + y=90$
equation 2: $y=x + 8$
b. $x = 41$, $y = 49$