Question

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

Answer 1

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

`m = (190)/(4) = 47.5`

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