In a triangle, if the second angle is 2 times the first angle and the third angle is 3 times the first angle, find the angles of a triangle.

Question

I understand angles etc very well, but I have no idea how to solve questions like this except with trial and error, which would take a while. Thank you.

Answer 1

For a triangle, we know that the sum of the interior angles must equal 180°.

Let x=the 1st angle

y=the 2nd angle

z=the 3rd angle

We have 3 unknowns, we must have 3 equations to solve for it.

Eq. I: x+y+z=180°

Eq. II: y=2x

Eq. III: z=3x

We can substitute the y and z values from Eq. II & III into Eq. I and solve for x:

x+y+z=180° Eq. I

x+2x+3x=180° substitute the values for y & z

6x=180° simplify

x=180°/6 divide both sides by 6 to isolate x

x=30° solve for x

Use this value of x to solve for y in Eq. II and z in Eq. III:

y=2x Eq. II

y=2(30) substitute for x

y=60° solve for y

z=3x Eq. III

z=3(30) substitute for x

z=90° solve for z

The answer is 30°, 60° and 90°.