Finding the measure of angle 3

In this problem, we need to find the measure of angle three. We can do this by examining the properties of the triangles and the intersecting lines in the diagram one by one.

Let's start with the isosceles triangle on the far left. Notice the hash marks on its two sides, which tell us it is isosceles.

In an isosceles triangle, the angles opposite the equal sides are also equal. Since the vertex angle is forty-eight degrees, the two base angles must sum to one hundred thirty-two degrees.

Dividing that by two, we find each base angle is sixty-six degrees.

Now, look at the base angle that is part of a larger straight line. Next to it is angle one. Since they are supplementary, they add up to one hundred eighty degrees.

Subtracting sixty-six from one hundred eighty, we find that angle one is one hundred fourteen degrees.

Wait, looking closer at the intersection, angle one and the base angle are actually adjacent on a line. Let's re-examine the center triangle containing angles one, two, and three.

Let's focus on the right-hand side first to find angle two. We see a right triangle with a ninety-degree angle and a sixty-five degree angle.

In this right triangle, the angles must sum to one hundred eighty degrees. So the angle at the far right is ninety minus sixty-five, which is twenty-five degrees.

Wait, the diagram labels the angle at the very end as angle four. For now, let's look at angle two. Angle two and sixty-five degrees form a linear pair.