The isosceles trapezoid is part of an isosceles triangle with a 34 degree vertex angle. what is the measure of an acute base angle of the trapezoid? of an obtuse base angle? the diagram is not drawn to scale.
a. 73; 107
b. 34; 146
c. 73; 146
d. 34; 107

The measure of an acute base angle of the trapezoid is 73 degrees and the measure of an obtuse base angle is 107 degrees and this can be determined by using the properties of a trapezoid and isosceles triangle.

Given :

The isosceles trapezoid is part of an isosceles triangle with a 34-degree vertex angle.

The following steps can be used in order to determine the measure of an acute base angle and an obtuse base angle of the trapezoid:

Step 1 - According to the property of an isosceles triangle the base angles are:

2x = 146

x = 73 degrees.

Step 2 - Now, the sum of the interior angle of a trapezoid is 360 degrees.

Step 3 - So, the measure of an acute base angle of a trapezoid is:

2y + 73 + 73 = 360

2y = 214

y = 107 degrees

So, the correct option is A).

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