a) Parallel for both line segments have the same slope = -5/4
b) 55º
Step-by-step explanation:
a) To verify the parallelism of these line segments, It's necessary to find the slope of each one. Parallel lines share the same slope value:
[tex]m_{BC}=\frac{0-150}{120-0}=-\frac{-5}{4}\\m_{AD}=\frac{0-125}{100-0}=-\frac{5}{4}[/tex]
b) If ∠DAB = 125°, what is the measure of ∠CBA? Justify your reasoning.
Those beams do not form a parallelogram because:
Using the formula of distance between those points
[tex]d=\sqrt{(y_{2}-y_1)^{2}-(x_{2}-x_{1})^2[/tex]
[tex]\overline {AB}=25\: \: \: \overline{CD}=20\: \: \overline{AD}=160 \: \: \overline{BC}=192[/tex]
So this is a trapezoid. And two adjacent angles within a trapezoid are supplementary, so If ∠DAB = 125º then 180 - ∠CBA=55º
