Prove a||b
A. m∠5 =40°
B. m∠2= 140°
C. ∠5 and ∠2 are supplementary angles
D. ∠5 and ∠2 are same-side interior angles
E. a||b
To prove that a||b, we need to show that the lines a and b are parallel. In order to do this, we will use the given information.
Since ∠5 and ∠2 are supplementary angles (C), we know that m∠5 + m∠2 = 180°. Given that m∠5 = 40° (A) and m∠2 = 140° (B), we can substitute these values into the equation to get:
40° + 140° = 180°
This equation is true, so we know that ∠5 and ∠2 are supplementary angles.
If two angles are supplementary and on the same side of a transversal line, as given by statements C and D, then the lines on which they lie are parallel. Therefore, we can conclude that a||b.
Therefore, given the information provided, we have proven that a||b.