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?

A1.Measure of angle AED is 36°

2.Base Angle Theorem

3.Corresponding angles are congruent

B1.Measure of angle AED is 54°

2.Base Angle Theorem

3.Alternate interior angles are congruent

C1.Measure of angle AED is 54°

2.Triangle Sum Theorem

3.Alternate interior angles are congruent

D1.Measure of angle AED is 54°

2.Triangle Sum Theorem

3.Corresponding angle are congruent

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Verified Answer :

syed514 syed514 · Answer 1 · 2016-12-11T03:32:05-05:00

Right answer is

D. 1.Measure of angle AED is 54°

2.Triangle Sum Theorem

3.Corresponding angle are congruent

Answer Link

pinquancaro pinquancaro · Answer 2 · 2018-10-16T03:04:53-04:00

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.