Question

A rectangle has dimensions 10 cm by 5 cm. Determine the measures of the angles at the point where the diagonal intersects.

a) 90°, 90°, 90°, 90°
b) 45°, 45°, 45°, 45°
c) 90°, 90°, 45°, 45°
d) 60°, 60°, 60°, 60°

Answer 1

The angles formed at the point where the diagonal of a rectangle intersects are two angles of 90°, and two angles of 45°, making the correct answer c) 90°, 90°, 45°, 45°.

Step-by-step explanation:

To determine the measures of the angles at the point where the diagonal of a rectangle intersects, we need to remember that the diagonals of a rectangle are equal and bisect each other. In a rectangle, each corner (or vertex) is a right angle (90°). When a diagonal is drawn, it creates two triangles within the rectangle. Each of these triangles is a right-angled triangle, with the hypotenuse being the diagonal itself.

The diagonal divides each corner in half, leading to angles of 45° each. Since we have two right angles at each end of the diagonal, and the diagonal bisects these angles, the correct answer will be two angles of 45° and two angles of 90°. Therefore, the answer is: c) 90°, 90°, 45°, 45°.