Question

A triangle has angle measures that are related as follows: -the largest angle is eight times the smallest angle -the middle angle is triple the smallest angle find the measurements of the angles.

Answer 1

The angles are 15 degrees, 45 degrees and 120 degrees

Explanation:

The triangle has three three sides and three angles. The sum of the angles in a triangle is 180 degrees

Let x = the size of the largest angle of the triangle

Let y = the size of the middle angle of the triangle

Let z = the size of the smallest angle of the triangle.

x + y + z = 180 - - - - -- - - - - - - 1

The size of the largest angle is eight times the size of the smallest angle.

This means

x = 8z

The size of the middle angle is triple the size of the smallest angle. This means

y = 3z

Put x = 8z and y = 3z in equation 1

8z + 3z + z= 180

12z = 180

z = 180/12 = 15

x = 8z = 8×15 = 120

y = 3z = 3 × 15 = 45