Question

The measure of one angle is six more than half the measure of another angle. If the angles are complimentary, find both angle measures.

Answer 1

12.8571°

and

77.1429°

Explanation:

Complementary angles sum 90°

a = 6b Eq. 1

a + b = 90 Eq. 2

Replacing Eq. 1 in Eq. 2:

6b + b = 90

7b = 90

b = 90/7

b = 12.8571° (aprox)

From Eq. 1:

a = 6*b

a = 6*12.8571

a = 77.1429°

Check:

from Eq. 2:

a + b = 90

77.1429° + 12.8571 = 90°

Answer 2

One angle is 42 and the other angles in 48

Explanation:

Let x = one angle

Let y = the other angle

x + 6 = y

x + y = 90 Complementary angles add to 90.

Substitute x + 6 for y in the second equation.

x + y = 90

x + x + 6 = 90 Combine the x's

2x + 6 = 90 Subtract 6 from both sides of the equation.

2x = 84 Divide both sides by 2

x = 42

x + y = 90 Substitute 42 in for x

42 + y = 90 Subtract 42 from both sides

y = 48