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 47°. Triangle abc with segment de. Angle ade measures 47 degrees. The proof, with a missing reason, proves that the measure of angle ecb is _____.

Answer 1

The measure of angle ECB in the right-angled triangle ABC with midpoints D and E on sides AB and AC, respectively, and angle ADE measuring 47°, is also 47°.

Step-by-step explanation:

The question refers to a right-angled triangle named ABC, with midpoints D and E on sides AB and AC, respectively. To find the measure of angle ECB, we can utilize the fact that triangle ADE is similar to triangle ECB since they both share angle A and have a right angle.

Given that angle ADE measures 47° and the sum of angles in a triangle is always 180°, angle AED, being opposite the hypotenuse DE, must also measure 47°. Since angle A is common in both triangles, the measure of angle A must be 180° - 90° - 47° = 43°.

Using triangle ECB now, the angle ECB must be 90° - 43° = 47°, as it is the complement of angle A in this triangle.