Question

One angle of a triangle is twice as large as another. The measure of the third angle is 60° more than that of the smallest angle. Find the measure of each angle.

The measure of the smallest angle is º


Please help :)

Answer 1

The measure of the smallest angle is 30º

Explanation:

Let the angles be:

`x \to` the first angle (the smallest)

`y \to` the second angle

`z \to` the third angle

So, we have:

`y = 2x`

`z=x + 60`

Required

Find x

The angles in a triangle is:

`x + y +z = 180`

Substitute values for y and z

`x + 2x +x + 60 = 180`

`4x + 60 = 180`

Collect like terms

`4x = 180-60`

`4x = 120`

Divide by 4

`x = 30`