Question

One angle of a triangle measures 75°. The other two angles are in a ratio of 10:11. What are the measures of those two angles?

Answer 1

One angle of a triangle measures 75°. The other two angles are in a ratio of 10:11. What are the measures of those two angles?

One angle measures = 75°

Ratio of other 2 angles = 10 : 11

Let the number be x

So, 10x : 11x

Sum of interior angles of a triangle = 180°

Now,

`75 + 10x + 11x = 180`

`10x + 11x = 180 - 75`

`10x + 11x = 105`

`21x = 105`

`x = 105/21`

`x = 5`

So,

Second angle = 10x = 10 × 5 = 50° ans

Third angle = 11x = 11 × 5 = 55° ans