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Tcecarenko [31]
3 years ago
9

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

Mathematics
1 answer:
nata0808 [166]3 years ago
4 0

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



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