MATH SOLVE

3 months ago

Q:
# What is the value of x? Identify the missing justifications.mPQR= x+11, mSQR=x+7, and mPQS=100mPQR+SQR=mPQS a. __________x + 11 + x + 7 = 100 b. Substitution Property2x + 18 = 100 c. Simplify2x = 82 d. __________x = 41 e. Division Property of EqualityA.Angle Addition Postulate; Subtraction Property of EqualityB.Protractor Postulate; Addition Property of EqualityC.Angle Addition Postulate; Addition Property of EqualityD.Protractor Postulate; Subtraction Property of Equality

Accepted Solution

A:

The correct answer is:A.Angle Addition Postulate; Subtraction Property of Equality
Explanation:The angle addition postulate states that if you place two angles side by side, then the measure of the resulting angle will be equal to the sum of the two original angle measures. This gives us m∠PQR+m∠SQR = m∠PQS.The next missing justification is for the step that takes 2x+18=100 to 2x=82. In order to get here, we subtract 18 from each side; the property that allows this is the subtraction property of equality.