Problema Solution
One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 10 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
Answer provided by our tutors
let
x = the smallest angle
y and z the other two angles of the triangle
One angle in a triangle has a measure that is three times as large as the smallest angle:
y = 3x
The measure of the third angle is 10 degrees more than that of the smallest angle:
z = 10 + x
since the sum of the angles in a triangle is 180 we have:
x + y + x = 180
plug the values for y and z into the last equation:
x + 3x + (10 + x) = 180
by solving we find:
x = 34 degrees
click here to see the step by step solution of the equation:
y = 3*34
y = 104 degrees
z = 10 + 34
z = 44 degrees
since 104 > 44 > 34
the largest angle is 104 degrees.