This triangle is an isosceles triangle. That means that the two base angles are equal.
You can set the two expressions equal to each other.
15x-13=8x+29
Solving this, you will find that x=6
Now you can plug x into the two expressions.
15(6)-13=77
8(6)+29=77
Those are the measurements of the two angles.
To find the last angle, you know that the angles of any triangle add up to 180 degrees. Using this information, you can add up the 3 angle measurements and set them equal to 180.
77+77+2y=180
y=13
Now plug in y.
2(13)=26
THe three angle measures are 77, 77, and 26