Mila earns money each week by tutoring and by babysitting. She charges twice as
much per hour of tutoring as per hour of
babysitting. This week, she works 8
hours. If she charges $13 per hour of
tutoring and earns $84.50 this week,
how many hours does she tutor?

m<1 = 57°

m<2 = 33°

Step-by-step explanation:

To find the numerical measure of both angles, let's come up with an equation to determine the value of x.

Given that m<1 = (10x +7)°, and m<2 = (9x - 12)°, where both are complementary angles, therefore, it means, both angles will add up to give us 90°.

Equation we can generate from this, is as follows:

(10x + 7)° + (9x - 12)° = 90°

Solve for x

10x + 7 + 9x - 12 = 90

Combine like terms

19x - 5 = 90

Add 5 to both sides

19x = 90 + 5 (addition property not equality)

19x = 95

Divide both sides by 19

x = 5

m<1 = (10x +7)°

Replace x with 5

m<1 = 10(5) + 7 = 50 + 7 = 57°

m<2 = (9x - 12)

Replace x with 5

m<2 = 9(5) - 12 = 45 - 12 = 33°