# Thread: Angles in a triangle

1. ## Angles in a triangle

It's a bit hard for me to translate math problems to english, but I think you'll be able to understand it:

Points A, B and C are on a circle. The arc between A and B is 1/12 of the circle's perimeter, the arc between B and C is 1/6 of the perimeter. What are the angles of the triangle ABC?

Oh yeah, is this even in the correct section of the forum?

2. Originally Posted by Trikotnik
It's a bit hard for me to translate math problems to english, but I think you'll be able to understand it:

Points A, B and C are on a circle. The arc between A and B is 1/12 of the circle's perimeter, the arc between B and C is 1/6 of the perimeter. What are the angles of the triangle ABC?

Oh yeah, is this even in the correct section of the forum?
familiar with the angle measures of arcs?

each angle is an inscribed angle in the circle ... there is a theorem that states that an inscribed angle is 1/2 the measure of its intercepted arc.

angle A = 1/2 of arc BC

angle B = 1/2 of major arc AC

angle C = 1/2 of arc AB

3. We know that the circumference of a circle is, C=2*$\displaystyle \pi$*r. Using the information given in the problem, this means that the length of the arc between A and B is (r*$\displaystyle \pi$)/6 and between B and C is (r*$\displaystyle \pi$)/3.

Secondly, we know that s=r*$\displaystyle \theta$ where s is the arc length, r is your radius, and $\displaystyle \theta$ is the angle.

Rearranging the above equation will allow you to solve for two of the angles. Simply subtracting them from the total degrees in a triangle will give you the third.

4. @cheme
But how can I use any of the equations containing r if I don't have the lenght of the radius? Should I just make it up?

Is it even possible to solve this without any additional information?

Edit: @skeeter
I just realised what a major arc is. Thanks. Problem Solved.

α=30°
β=135°
γ=15°

5. Just wanted to say that I passed the test. Thanks a lot, skeeter, I'll definitely recommend this portal to friends.