A baseball diamond home plate has three right angles the other angles are congruent find their measure?

As the home plate has 5 angles it is a pentagon.

The angles of a pentagon sum to (5 - 2) × 180° = 3 × 180° = 540°

Three angles are right angles, and their sum is 3 × 90° = 270°

This leaves 540° - 270° = 270°

As the remaining two angles are congruent, they are each half of this at 270° ÷ 2 = 135°

The remaining angles are 135° each.