Question

4. A rectangle is inscribed into a circle. The rectangle is cut along one of its diagonals and reflected across that diagonal to form a kite. Draw the kite and its diagonals. Find all the angles in this new diagram, given that the acute angle formed by the diagonal of the rectangle in the original diagram was 40°.

Answer 1

The diagrams below explain the process with angles.

Explanation:

In figure 1, a rectangle is drawn in the circle.

Since the acute angle being drawn by the hypotenuse is 40 degree in figure 2, thus we can say the other angle will be 50 degrees.

In figure 3, the rectangle is cut across its diagonal to form a kite shaped entity within the circle.

Now we know that m∠BDE = 40° = m∠ADB.

Also, m∠A = m∠E = 90°

Thus, m∠EBD = m∠ABD = 50° ⇒ m∠B = 100°

Also, m∠ADE = 80° ANSWER