Answer:

Step-by-step explanation:

It is given that 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°.

To prove: The measure of angle ECB is 43°.

Proof:

Statement                                                          Reason

1. m∠ADE=47°                                                     Given

2. m∠DAE=90°                                        definition of right angle

3. In ΔADE, ∠ADE+∠DAE+∠DEA=180°      

⇒47+90+∠DEA=180°

∠DEA=43°                                              triangle sum theorem

4. ∠ECB=43°                                              substitution property

5.Segment DE joins the midpoints

of segment AB and AC                                        Given

6. Segment DE is parallel to segment BC        Midsegment theorem

7. m∠ECB≅m∠AED                                Corresponding angles are congruent

therefore, Measure of angle AED is 43°.

Hence proved.

Hence, option A is correct.