Find the sizes of the three unknown angles in the image below.
Give your answers in degrees.
34 degrees
First, we need to recognize that the two smaller angles at the bottom of the triangle are equal, since they are opposite equal sides. Therefore, each of those angles is:
180 - 90 - 34 = 56 degrees
Next, we can use the fact that the angles in a triangle add up to 180 degrees to find the remaining angle at the top of the triangle:
180 - 56 - 56 = 68 degrees
So the three unknown angles are:
56 degrees, 56 degrees, and 68 degrees.