Question

One angle of a triangle measures 75°. The other two angles are in a ratio of 2:5. What are the measures of those two angles?

Answer 1

well, since a triangle has a total of 180° interior angles, that means 180 - 75 = 105 is leftover for the other two remaining angles.

now, they're in a 2 : 5 ratio, well, let's simply divide 105° by (2 + 5) and distribute accordingly.

`2~~ : ~~5\implies 2\cdot (105)/(2+5)~~ : ~~5\cdot (105)/(2+5)\implies 2\cdot 15~~ : ~~5\cdot 15\implies \text{\LARGE 30~~ : ~~75 }`