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
[tex]m = \frac{190}{4} = 47.5[/tex]
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
