Question

Finding Unknown Measurements
Another engineer is tiling a new building. A square tile is cut along one of its diagonals to form two triangles with two congruent angles. What are the measurements of the interior angles of the triangles? Explain how you calculated them.

Answer 1

A square's corner is 90°. Cutting along a diagonal leaves a triangle with the two equal sides of the square as its legs, so the triangle is isosceles and the two acute angles are congruent. Let each acute angle be x. Then x + x + 90° = 180°, so 2x = 90° and x = 45°.

Thus each triangle's interior angles are 90°, 45°, and 45°.