Question

Which statement and reason can be used to fill in the numbered blank spaces

Answer 1

Right answer is

D. 1.Measure of angle AED is 54°

2.Triangle Sum Theorem

3.Corresponding angle are congruent

Answer 2

Statement 1 is 'corresponding angles are congruent'.

Statement 2 is 'Triangle sum theorem'

Statement 3 is ∠AED = 22°.

Explanation:

We are given the flowchart which proves that ∠ECB = 22°

Now, the statement corresponding to 1. is '∠ECB ≅ ∠AED'.

This happens because the two line DE and BC are parallel and the corresponding angles of two parallel lines are congruent.

So, statement 1 is 'corresponding angles are congruent'.

Now, the statement corresponding to 2 and 3 are ∠ADE = 68° and ∠DAE = 90°.

After these statement we get that ∠ECB = 22°.

This happens because the sum of all three angles in a triangle is 180°.

Therefore, ∠ADE + ∠DAE + ∠AED = 180°

i.e. 68° + 90° + ∠AED = 180°

i.e. ∠AED = 180° - 158°

i.e. ∠AED = 22°

So, statement 2 is 'Triangle sum theorem' and statement 3 is ∠AED = 22°.