Notice that the angles in the triangle ABC are labeled:
x, 2x , and 60 degrees.
Then, we need to use the property that tells us that the addition of all internal angles in a triangle add to 180 degrees.
Then we can create the following equation:
x + 2 x + 60 = 180
combine like terms
3 x + 60 = 180
subtract 60 from both sides
3 x = 120
divide both sides by 3 to isolate x completely
x = 120 / 3
x = 40
So we know that x is 40 degrees, so angle angle
Now, you were told that triangles ABC and EHG were similar, which means that the corresponding angles must be of the same measure:
.
Therefore, if we are asked to find the measure of angle , which is the same as angle H, we need to type 80 degrees.