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°.
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?

A. 1.Measure of angle AED is 36°
2.Base Angle Theorem
3.Corresponding angles are congruent

B. 1.Measure of angle AED is 54°
2.Base Angle Theorem
3.Alternate interior angles are congruent

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

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

Answer 1

Observe the given figure.

Given: 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°.

Consider triangle ADE,

By Triangle Sum Theorem, we get

$\angle ADE + \angle DEA + \angle DAE = 180^\circ$

$36^\circ + \angle DEA + 90^\circ = 180^\circ$

$126^\circ + \angle DEA = 180^\circ$

$\angle DEA = 54^\circ$

Now, we have to determine the measure of angle ECB.

Since, line DE is parallel to BC

So, $\angle AED = \angle ECB$ (corresponding angles are equal)

So, Angle ECB is 54 degrees.

So, Option D is the correct answer.

Answer 2

Right answer is

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