Question

"Given that <1 and <2 are complementary and:

m<1 = 12q - 9
m<2 = 8q + 19
Find q and the measures of each angle.
A) q = 3, m<1 = 27 degrees, m<2 = 43 degrees
B) q = 4, m<1 = 39 degrees, m<2 = 51 degrees
C) q = 2, m<1 = 15 degrees, m<2 = 35 degrees
D) q = 5, m<1 = 51 degrees, m<2 = 59 degrees"

Answer 1

To find q and the measures of angles 1 and 2 in the given complementary angles, set up a system of equations based on their formulas. Solve the system of equations to find q = 4 and angle 1 = 39 degrees, angle 2 = 51 degrees.

Step-by-step explanation:

To solve for q and the measures of each angle, we can set up a system of equations using the given information. Since angles 1 and 2 are complementary, we know that the sum of their measures is 90 degrees.

Equation 1: m1 = 12q - 9

Equation 2: m2 = 8q + 19

Setting up the system of equations:
m1 + m2 = 90
12q - 9 + 8q + 19 = 90

Combine like terms:
20q + 10 = 90

Subtract 10 from both sides:
20q = 80

Divide by 20:
q = 4

Finally, substitute q = 4 into the equations to find the measures of the angles:
m1 = 12(4) - 9 = 48 - 9 = 39 degrees
m2 = 8(4) + 19 = 32 + 19 = 51 degrees