Given: ∠ABC and ∠CBD are supplementary angles. m∠ABC = 4x + 7, m∠CBD = 2x − 1. Prove: m∠ABC = 123
How do I write this in a two column proof?
What does angle CBD measure
4x+7 + 2x-1=180
6x=172
x=28.5
4x+7=123
What does angle CBD measure
4x+7 + 2x-1=180
6x=172
Round up from 28.6
x=29
4(29)+7=123
2(29)-1=57
To write a two-column proof, you need to present the statements (each representing a fact or a step) in one column, and the reasons (justifications or logical connections) in the second column. Here's how you can write a two-column proof to show that m∠ABC = 123:
Statement | Reason
-----------------|-----------------
m∠ABC = 4x + 7 | Given
m∠CBD = 2x − 1 | Given
m∠ABC + m∠CBD = 180° | Supplementary angles
4x + 7 + 2x − 1 = 180° | Substitution
6x + 6 = 180° | Combine like terms
6x = 174° | Subtracting 6 from both sides
x = 29° | Dividing both sides by 6
m∠ABC = 4(29) + 7 | Substitution
m∠ABC = 123° | Simplification
In this proof, we start by stating the given information: m∠ABC = 4x + 7 and m∠CBD = 2x - 1. Then, we apply the fact that supplementary angles add up to 180° (m∠ABC + m∠CBD = 180°) as our third statement, which links the two given angles. We then combine like terms and simplify the equation to solve for x.
Once we find the value of x as 29°, we substitute it back into the original equation for m∠ABC to find the measure of the angle. Finally, simplifying the expression, we can conclude that m∠ABC is indeed equal to 123°.