Question

the following flowchart with missing statements and reasons proves that the measure of angle ecb is 54°. which statement and reason can be used to fill in the numbered blank spaces? 1 measure of angle aed is 36° 2 base angle theorem 3 corresponding angles are congruent 1 measure of angle aed is 54° 2 base angle theorem 3 alternate interior angles are congruent 1 measure of angle aed is 54° 2 triangle sum theorem 3 alternate interior angles are congruent 1 measure of angle aed is 54° 2 triangle sum theorem 3 corresponding angles are congruent

Explanation:

Step1: Find angle AED in triangle ADE

In right - triangle ADE, $\angle DAE = 90^{\circ}$ and $\angle ADE=36^{\circ}$. By the Triangle Sum Theorem (the sum of the interior angles of a triangle is $180^{\circ}$), we have $\angle AED=180^{\circ}-\angle DAE - \angle ADE=180^{\circ}-90^{\circ}-36^{\circ}=54^{\circ}$.

Step2: Determine the relationship between $\angle ECB$ and $\angle AED$

Since segment DE is parallel to segment BC (by the Mid - segment theorem) and $\angle ECB$ and $\angle AED$ are corresponding angles, corresponding angles are congruent when two parallel lines are cut by a transversal.

Answer:

1. Measure of angle AED is 54°
2. Triangle Sum Theorem
3. Corresponding angles are congruent