Question

One angle of a linear pair is 10 more than two-thirds the other angle. Find the measure of both angles.

Answer 1

Answer:

102° and 78°

Step-by-step explanation:

let one angle be x then the other angle is

$\frac{2}{3}$ x + 10 ( 10 more than two-thirds the other angle )

A linear pair of angles sum to 180°, hence

x + $\frac{2}{3}$ x + 10 = 180

$\frac{5}{3}$ x + 10 = 180 ( subtract 10 from both sides )

$\frac{5}{3}$ x = 170

multiply both sides by 3 and divide by 5

5x = 510

x = 102

The 2 angles are x = 102° and

$\frac{2}{3}$ x + 10 = $\frac{2}{3}$ × 102 + 10 = 68 + 10 = 78°

As a check : 102 + 78 = 180 → correct