Answer:
102° and 78°
Step-by-step explanation:
let one angle be x then the other angle is
[tex]\frac{2}{3}[/tex] x + 10 ( 10 more than two-thirds the other angle )
A linear pair of angles sum to 180°, hence
x + [tex]\frac{2}{3}[/tex] x + 10 = 180
[tex]\frac{5}{3}[/tex] x + 10 = 180 ( subtract 10 from both sides )
[tex]\frac{5}{3}[/tex] x = 170
multiply both sides by 3 and divide by 5
5x = 510
x = 102
The 2 angles are x = 102° and
[tex]\frac{2}{3}[/tex] x + 10 = [tex]\frac{2}{3}[/tex] × 102 + 10 = 68 + 10 = 78°
As a check : 102 + 78 = 180 → correct
