Question

What are the missing reasons in the proof?

Answer 1

D. Sum of Interior angles; Converse of opposite angles theorem.

Explanation:

Solution:

Statement Reasons

1. m∠A =50°,m∠B= 130°,m∠C = 50° Given

Now we know that;

"Sum of all interior angles is 360°."

2. m∠A + m∠B + m∠C + m∠D =360° Sum of all Interior angles

3. 50°+ 130° + 50° + m∠D =360° Substitution

4. m∠D =130° Subtraction property of equality.

5. m∠A Congruent m∠C Angles with equal measure are congruent m∠B Congruent m∠D

Now By Converse of opposite angle theorem which states that;

"If the opposite angles of a quadrilateral are congruent, then the figure is a parallelogram."

6. ABCD is Parallelogram Converse of opposite angle theorem