Question

Triangle abc is a right triangle. Point d is the midpoint of side ab and point e is the midpoint of side ac. The measure of angle ade is 36°. Triangle abc with segment de. Angle ade measures 36 degrees. The proof, with a missing reason, proves that the measure of angle ecb is _____.

1) 54°
2) 72°
3) 90°
4) 108°

Answer 1

The measure of angle ECB is 36 degrees.

Step-by-step explanation:

To find the measure of angle ECB, we can use the fact that triangle ABC is a right triangle. Since angle A is a 90-degree angle, angle ACE is also a 90-degree angle (because EC is perpendicular to AC). Since angle Ade is 36 degrees, the measure of angle ECA is 90 - 36 = 54 degrees. Since triangle ECB is a right triangle, the sum of angles ECA and ECB is 90 degrees. Therefore, the measure of angle ECB is 90 - 54 = 36 degrees.