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.
73; 107
34; 146
73; 146
34; 107

Solution:

Given, the isosceles trapezoid is part of an isosceles triangle with a 34 degree vertex angle.

We have to find the measure of an acute base angle of the trapezoid.

An isosceles triangle is a triangle that has two sides of equal length.

By angle sum property of a triangle,

The sum of all three interior angles of a triangle is equal to 180 degrees.

Now, 34° + x + x = 180°

2x = 180° - 34°

2x = 146°

x = 146°/2

x = 73°

The measure of an acute base angle of the trapezoid is 73 degrees.

We know that the sum of the interior angles of a trapezoid is equal to 360 degrees.

So, y + y + 73 + 73 = 360°

2y + 146° = 360°

2y = 360° - 146°

2y = 214°

y = 214°/2

y = 107°

Therefore, the measure of an obtuse angle of the trapezoid is 107 degrees.

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.

Summary:

The isosceles trapezoid is part of an isosceles triangle with a 34 degree vertex angle. The measure of an acute base angle of the trapezoid is 73 degrees. The measure of an obtuse base angle is 107 degrees.