Fill in the missing statements and reasons to complete the following proof
2. 229 + m∠X = 360.
3. 49+ 131 +49 + m<x = 360 substitution property of equality
4. 229+ m<x = 360
5. m<x= 131
6. <X ≅ <Z and <W ≅ <Y Angles with equal measures are congruent
7. WXYZ is a parallelogram.
To complete the missing statements and reasons in the given proof, we need to make logical deductions based on the information given. Let's complete the proof step by step:
1. Given: WXYZ is a parallelogram.
2. Given: m∠X + m∠Z = 180. (This is the property of the opposite angles of a parallelogram.)
3. Given: m∠W + m∠Y = 180. (This is the property of the opposite angles of a parallelogram.)
4. Given: m∠X + m∠Y + m∠Z + m∠W = 360. (This is the property of the sum of the angles in a quadrilateral.)
5. Given: 229 + m∠X = 360. (From statement 2.)
6. Substitution property of equality: 229 + m∠X = 360 = m∠X + 229. (We can switch the order of the terms since addition is commutative.)
7. Subtract 229 from both sides: 229 + m∠X - 229 = 360 - 229.
8. Simplify: m∠X = 131.
9. Given: m<x = 131. (From step 8.)
10. Angle subtraction property: m∠W = 180 - m∠X = 180 - 131 = 49. (This property states that the measure of an angle is equal to the difference between 180 degrees and the measure of its supplementary angle.)
11. Angle subtraction property: m∠Y = 180 - m∠X = 180 - 131 = 49. (Using the same property as in step 10.)
12. Congruent angles: <X ≅ <Z and <W ≅ <Y. (Angles with equal measures are congruent.)
13. Given: <X ≅ <Z and <W ≅ <Y. (From step 12.)
14. Given: WXYZ is a parallelogram. (Given in the initial statement.)
By completing these steps, we have filled in the missing statements and reasons to complete the proof.