The complete proof statement and reason for the required proof is as follows:
Statement Reason
m<PNO = 45 Given
MO Given
<MNP and <PNO are a
linear pair of angles Definition of linear pairs of angles
<MNP and <PNO are
supplementary angles Linear Pair Postulate
m<MNP + m<PNO = 180° Definition of supplementary angles
m<MNP + 45° = 180° Substitution property of equality
m<MNP = 135° Subtraction property of equality
Answer:
10 and 13
Step-by-step explanation:
Let the two numbers be p and q. p = (1/2)q + 8. p + q = 23. Substituting (1/2)q + 8 for p, we get (1/2)q + 8 + q = 23.
First, subtract 8 from both sides, obtaining (1/2)q + q = 15.
Next, mult. all terms by 2 to eliminate the fraction (1/2): q + 2q = 30.
Then 3q = 30, and q = 10. Then p = (1/2)(10) + 8 = 5 + 8 = 13.
The numbers are 10 and 13.
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