Question

↔XY || ↔MN. ↔PQ is the transversal. ↔PQ intersects ↔XY at point A and ↔MN at point B. If LNBP = 55°, find the measure of the remaining angles.

Answer 1

I've attached an image for reference. There I've shown the measure of all the angles.

First of all let me tell you by the term Transversal we mean when two parallel lines are intersected at some point by a third line.

Acc to the data angle YAP = 55 degree since it is corresponding to angle NBP.

angle QBM = 55 degree since it is vertically opposite to angle NBP.

Similar is the case for angle XAB = 55 degree.

Now we know that angle XAP and YAB will be the same. Also their sum will be 360 - (55 + 55) = 250.

Therefore, angle XAP + angle YAB = 250/2 = 125 degree.

Same will be the value of angle MBP and angle QBN = 125 degree