Complete the two-column proof.
Given: m angle RST=5x degrees and m angle UVW=7x degrees angle RST and angle UVW are supplementary
Prove: x =15
statement: m angle RST=5x degrees and m angle UVW=7x degrees angle RST and angle UVW are supplementary reason: given
Statement: mangle RST +m angle UVW=180 reason: definition of supplementary angles
Statement:5x + 7x = 180 reason: a._______________
statement:12x = 180 reason: b._______________
Statement: x=15 reason: c._______________
Reasons:
a. Substitution property (substituting the measures of angle RST and angle UVW from the previous statements)
b. Simplification (combining like terms)
c. Division property of equality (dividing both sides of the equation by 12)
a. Combining like terms (5x + 7x) according to the distributive property.
b. Simplifying the equation by adding the terms on the left side of the equation (12x) according to the addition property of equations.
c. Dividing both sides of the equation by 12 in order to isolate x and solve for it, using the division property of equations.
a. Combining like terms, we have 12x = 180. This step is the result of adding the measures of angles RST and UVW together.
b. Dividing both sides of the equation 12x = 180 by 12 gives us x = 15. This step is the result of dividing both sides of the equation by 12 to isolate x.
c. Therefore, we have proven that x = 15 based on the given information and the reasoning provided in steps a and b.