Question

The isosceles trapezoid is part of an isosceles triangle with a 42 degree vertex

What is the measure of an obtuse base angle of the trapezoid? The diagram is not drawn to scale
PLEASE HELP ME SOLVE Questions 5. And 6. !!! Please

Answer 1

the measure of the obtuse base angle of the trepezoid is 111.

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.