Question

First, Nick used the linear pair postulate to determine m∠JKH + m∠JKN = 180°. Then, he said m∠MNH + m∠JKN = 180° because parallel lines make same-side interior angles supplementary.

What could be the next step in a valid proof of Nick's claim?

A.
m∠JKH + m∠JKN + m∠MNH = 180° because of the definition of supplementary angles.
B.
m∠JKH + m∠JKN = m∠MNH + m∠JKN because of the angle addition postulate.
C.
m∠JKH + m∠JKN = m∠MNH + m∠JKN because of the transitive property.
D.
m∠JKH + m∠JKN + m∠MNH = 180° because of the angle addition postulate.

Answer 1

B.

m∠JKH + m∠JKN = m∠MNH + m∠JKN because of the angle addition postulate.

Step-by-step explanation:

The next step in a valid proof of Nick's claim would be option B, which states that m∠JKH + m∠JKN = m∠MNH + m∠JKN because of the angle addition postulate.

This step is valid because the angle addition postulate states that the measure of an angle formed by two adjacent angles is the sum of the measures of the two angles. In this case, m∠JKN is adjacent to both m∠JKH and m∠MNH, so the sum of m∠JKH and m∠JKN is equal to the sum of m∠MNH and m∠JKN.

A.

If ∠a 160° + ∠b 20° = 180°

then If ∠a + ∠b = are supplementary

C.

transitive property

If x = y and y = z, then x = z.

For example, if 3 + 4 = 7 and 7 = 2 + 5, then 3 + 4 = 2 + 5.

The angle addition postulate is a basic principle in geometry that states that the measure of an angle formed by two adjacent angles is equal to the sum of the measures of those angles. Here are a few examples of how the angle addition postulate can be used:

D.

If ∠a + ∠b = adjacent

If ∠a 60° + ∠b 20° = ∠c

then ∠c = 80°

measure of an angle formed by two adjacent angles is equal to the sum of the measures of those angles

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