Question

in △abcd, find b in terms of a and c. after you pick your answer press go. a. b = 180 - a - c b. b = a + c c. b = -c - a d. b = a - c e. b = c - a

Explanation:

Step1: Use the property of parallelogram

In parallelogram \(ABCD\), \(AB\parallel CD\).

Step2: Use the property of alternate - interior angles

Since \(AB\parallel CD\), the angle at \(B\) (in \(\triangle ABD\)) and the angle formed by the transversal \(BD\) with \(AB\) and \(CD\) gives that the angle at \(A\) and the angle at \(C\) (in the triangle part) relate to \(b\).
We know that in a parallelogram, \(BC\parallel AD\). Also, in \(\triangle ABD\), the sum of angles in a triangle is \(180^{\circ}\). But using the property of parallelogram \(AB\parallel CD\), we have that the angle at \(A\) (in the triangle) and the angle \(c\) (in the triangle) and the angle \(b\) (since \(AB\parallel CD\), the angle corresponding to the sum of angles in the triangle - like part related to the parallelogram) gives \(b=a + c\) (because of the property that when a transversal cuts two parallel lines, the exterior angle is equal to the sum of the non - adjacent interior angles. Here, if we consider the transversal \(BD\) cutting \(AB\) and \(CD\) in parallelogram \(ABCD\), the angle \(b\) (at \(D\)) is equal to the sum of the angle \(a\) (adjacent angle in the part of the figure) and angle \(c\) (non - adjacent angle in the part of the figure) due to the parallel side property of parallelogram).

Answer:

B. \(b = a + c\)