One angle of a triangle is 27° . How many degrees must one of the other angles be for the Pythagorean Theorem to be true for the triangle?

Answer 1

In a triangle, the sum of the measures of all three angles is 180°.

Let's denote the measures of the other two angles as x and y. We know that one angle is 27°, so we have:

27 + x + y = 180

If the Pythagorean Theorem is true for the triangle, it means that the triangle is a right triangle. In a right triangle, one of the angles is 90°. Therefore, one of the other angles must be 90° for the Pythagorean Theorem to be true.

If we substitute 90 for x in the equation above, we can solve for y:

27 + 90 + y = 180

117 + y = 180

y = 180 - 117

y = 63

So, one of the other angles must be 63° for the Pythagorean Theorem to be true for the triangle.