Consider the diagram and proof below.

given: wxyz is a parallelogram, zx ≅ wy
prove: wxyz is a rectangle

statement

reason
1. wxyz is a ▱; zx ≅ wy 1. given
2. zy ≅ wx 2. opp. sides of ▱ are ≅
3. yx ≅ yx 3. reflexive
4. △zyx ≅ △wxy 4. sss ≅ thm.
5. ∠zyx ≅ ∠wxy 5. cpctc
6. m∠zyx ≅ m∠wxy 6. def. of ≅
7. m∠zyx + m∠wxy = 180° 7. ?
8. m∠zyx + m∠zyx = 180° 8. substitution
9. 2(m∠zyx) = 180° 9. simplification
10. m∠zyx = 90° 10. div. prop. of equality
11. wxyz is a rectangle 11. rectangle ∠ thm.

what is the missing reason in step 7?

triangle angle sum theorem
quadrilateral angle sum theorem
definition of complementary
consecutive ∠s in a ▱ are supplementary
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