**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.**