Video Transcript
Is the measure of angle π΄π·π less than, equal to, or greater than the measure of angle π΄πΆπ·?
Letβs begin by identifying the two angles that are referred to in the question. Angle π΄π·π is the angle formed by travelling from π΄ to π· to π. So itβs the obtuse angle marked in orange. Angle π΄πΆπ· is the angle formed by travelling from π΄ to πΆ to π·. So itβs the obtuse angle marked in green. Now, letβs consider how to answer this question.
We havenβt been given the length of any sides in the diagram or any of the angles. And therefore, we canβt answer this question by calculating the two angles. Instead, we need to think about the relationship between the measures of these two angles based on their positions. Letβs consider part of the diagram: triangle π΄πΆπ·.
With respect to this triangle, we see that angle π΄πΆπ· is an interior angle and angle π΄π·π is an exterior angle. We can therefore answer this question using the exterior angle inequality, which tells us about the relationship between the measure of an exterior angle of a triangle and the measures of the two nonadjacent interior angles.
The exterior angle inequality tells us that in a triangle the measure of an exterior angle is greater than each of the two nonadjacent interior angles. By nonadjacent interior angles, we mean the two interior angles of the triangle that donβt lie on the straight line with the given exterior angle β the two angles that Iβve marked with stars. One of these is of course the angle weβre interested in β angle π΄πΆπ·.
Therefore, we can conclude that by the exterior angle inequality, the measure of angle π΄π·π is greater than the measure of angle π΄πΆπ·.
