Question

Each face of a pyramid is an isosceles triangle with a 72 degree vertex angle. What are the measures of the base​ angles?

Answer 1

Each base angle of an isosceles triangle with a 72-degree vertex angle is 54 degrees.

Step-by-step explanation:

To find the base angles of an isosceles triangle with a 72 degree vertex angle, we use the fact that the sum of angles in any triangle is 180 degrees. Since the triangle is isosceles, the base angles are equal. Subtracting the vertex angle from 180 degrees gives us the sum of the two base angles:

180 degrees - 72 degrees = 108 degrees

Now divide the sum by 2 to find the measure of each base angle:

108 degrees ÷ 2 = 54 degrees

Therefore, the measure of each base angle in the isosceles triangle is 54 degrees.

Answer 2

52° and 52°

Step-by-step explanation:

An isosceles triangle has two base angles that are congruent. So let x be the measure of the base angle so that by Triangle Angle-Sum Theorem, we can write: X+X+76=180 and next would be 2X+76=180 and then it would be 2X=104 and finally it would be X=52. So there for the measures of the base angles are 52° and 52°. There hoped it helped!!!!