In a scalene triangle the smallest angle is 10 less than the middle angle. the largest angle is twice the middle angle. find the measures of each angle

The measure of each angle is 37.5 degrees, 47.5 degrees and 95 degrees

Solution:

A scalene triangle is a triangle that has three unequal sides

Let the middle angle be "m"

Given that, smallest angle is 10 less than the middle angle

Smallest angle = middle angle - 10

Smallest angle = m - 10

Given that, the largest angle is twice the middle angle

Largest angle = twice the middle angle

Largest angle = 2m

By angle sum property of triangle,

Three angles of a triangle add to 180 degrees

Therefore,

Smallest angle + middle angle + largest angle = 180

m - 10 + m + 2m = 180

4m - 10 = 180

4m = 180 + 10

4m = 190

Therefore,

Largest angle = 2m = 2(47.5) = 95

Smallest angle = m - 10 = 47.5 - 10 = 37.5

Thus the measure of each angle is 37.5 degrees, 47.5 degrees and 95 degrees