SOLUTION: this is the question i need answered: -The isosceles trapezoid is part of an isosceles triangle with a 46" degree vertex angle. What is the measure of an acute base angle of the

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Question 396756: this is the question i need answered:
-The isosceles trapezoid is part of an isosceles triangle with a 46" degree vertex angle. What is the measure of an acute base angle of the trapezoid? Of an obtuse angle? The diagram is not to scale.
(then it shows a triangle with a midsegment and thats all.)
PLEASE HELP ME!
Thanks
Answer by Edwin McCravy(20056) (Show Source):
You can put this solution on YOUR website!
Let's draw it to scale. Here's the trapezoid:

and here is the rest of the isosceles triangle, of
which the isosceles trapezoid is a part:

Next we draw the midsegment, which splits the figure in
half. It splits the 46� vertex angle into two 23� angles,
and the green line is perpendicular to both bases of
the trapezoid:

Now we'll just look at the left half, which is a right triangle,
actually two right triangles:

Since the two acute angles of a right triangle are complementary,
the other acute angle in both right triangles is
90�-23� or 67�:

and the angle supplementary to the upper 67� angle is 180�-67� = 113�

So therefore the original isosceles trapezoid has an acute
angle of 67� and an obtuse angle of 113�: