The dormer window on a house is in the shape of an isosceles triangle. The angle at the top is 52". What are the measures of the angles at the base? Describe in detail
An isosceles triangle has two equal angles and two equal sides. In this case, the angle at the top of the dormer window is 52 degrees. Since the triangle is isosceles, the two base angles are also equal to each other.
To find the measure of the base angles, we need to remember that the sum of the angles in a triangle is always 180 degrees. Since we already know one angle (52 degrees), we can use this information to find the measure of the two base angles.
Let's denote the measure of the base angles as x. Since the triangle is isosceles, we know that the two base angles are equal to each other.
So, the sum of the angles in the triangle can be expressed as:
52 + x + x = 180.
Now, combine the like terms:
52 + 2x = 180.
Subtract 52 from both sides:
2x = 128.
Divide both sides by 2:
x = 64.
So, the measure of the two base angles in the dormer window is 64 degrees each.