Hello, beefsupreme!

The angles of a triangle are 50°, 60° and 70°,

and a circle touches the sides at

Calculate the angles of triangle . Code:

P
o
/ \
/50°\
/ \
/ \
/ \
/ * * * \
/* *\
* *
A o- - - - - - - - -o B
/ \ / \
/* \ / *\
/ * \ o / * \
/ * \ O / * \
/ \ / \
/ * \ / * \
/ * \ / * \
/ 60° * \ / * 70° \
Q o - - - - - - - * o * - - - - - - - o R
C

We have with

Circle is inscribed in the triangle

. . and is tangent to at respectively.

Draw segments and radii

are penpendicular to the sides of the triangle.

Since O is the center of the inscribed circle,

. . bisect , resp.

We have: .

Since is isosceles: .

Similarly, we find that: .

Therefore: .