Question

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

Sample Explanation:

Since the triangle shares an angle with the original square, the triangle has a right angle. Since the triangle has two angles that are congruent, the equation for the measures of all three angles is 90 + 2x = 180, and I found that x = 45. The angles in the triangle are 90°, 45°, and 45°.

Explanation:

Finding Unknown Angle Measures Assignment

Finding Unknown Measurements

Answer 2

The measurements of the interior angles of the triangles are 45°-90°-45°

Explanation:

we know that

A square is a quadrilateral with 4 equal sides and 4 interior angles of 90 degrees

The diagonal of a square bisect the square into two congruent isosceles right triangles

The two congruent legs of each isosceles right triangle is equal to the length side of the square

The measure of the base's angles of each isosceles right triangle is equal to 45 degrees, because the diagonal bisect the right angle of the square

therefore

The measurements of the interior angles of the triangles are 45°-90°-45°