Derek wrote the following paragraph proof for the Vertical Angles Theorem:

The sum of angle 1 and angle 4 and the sum of angle 3 and angle 4 are each equal to 180 degrees by the definition of supplementary angles. The sum of angle 1 and angle 4 is equal to the sum of angle 3 and angle 4 by the transitive property of equality. Angle 1 is equal to angle 3 _____________________.

Which phrase completes the proof?

Aby construction using a straightedge
Bby the definition of a perpendicular bisector
Cby the subtraction property of equality
Dby the vertical angles theroem

the answer is C. by the subtraction property of equality
proof:
The sum of angle 1 and angle 4 is equal to the sum of angle 3 and angle 4 by the transitive property of equality
A1 + A4 = A3 + A4 so A1 = A3 + A4 - A4, and A1 = A3

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OrethaWilkison OrethaWilkison · Answer 2 · 2018-11-21T03:09:43-05:00

Answer:

Option C is correct.

By the Subtraction Property of Equality.

Explanation:

Supplementary Angles: Two angles are Supplementary if the sum of the measure of angles is 180 degree.

Given:

\(m\angle 1+ m\angle 4 =180^{\circ}\)

\(m\angle 3+ m\angle 4 =180^{\circ}\) {By definition of supplementary angle} .......[1]

Transitive Property of equality:

If a=b and

b = c,

then a = c

By the transitive property,

[1} ⇒ \(m\angle 1+m\angle 4 =m\angle 3+m\angle 4\) ......[2]

Subtraction property of equality states that you subtract the same number from both sides of an equation.

Subtract \(m\angle 4\) from both the sides in [2];

\(m\angle 1+m\angle 4-m\angle4=m\angle 3+m\angle 4-m\angle 4\)

Simplify:

\(m\angle 1 =m\angle 3\) {By subtraction property of equality}

Therefore, the only phrase which completes the proof is; by the subtraction property of equality