Answer:
the measure of the obtuse base angle of the trepezoid is 111.
Step-by-step explanation:
An isosceles triangle has one vertex angle and two congruent base angles. Also, we know that the sum of all angles in a triangle must equal 180 degrees. So we can say that:
Vertex Angle + Base Angle + Base Angle = 180.
Vertex Angle + 2 x (Base Angle) = 180.
2 x (Base Angle) = 180 - Vertex Angle
2 x (Base Angle) = 180 - 42
2 x (Base Angle) = 138
Base Angle = 69
Also, we know that angles on one side of a straight line always add to 180 degrees.
So we can say that:
Base Angle + ? = 180
? = 180 - Base Angle
? = 180 - 69
? = 111
So, the measure of the obtuse base angle of the trepezoid is 111.
