DEFG is an isosceles trapezoid. Find the measure of <E.
DEFG is an isosceles trapezoid. Find the measure of E.
What additional information would prove that DEFG is an isosceles trapezoid?
To find the measure of angle E in an isosceles trapezoid DEFG, you can use the properties of isosceles trapezoids.
An isosceles trapezoid has two opposite sides that are parallel and two opposite angles that are congruent. Let's call the parallel sides AB (top) and CD (bottom), and the angles at the ends of the parallel sides A and D.
In an isosceles trapezoid, the angles at the bases (E and F) are supplementary, meaning they add up to 180 degrees. Therefore, we can say that angle E + angle F = 180 degrees.
Now, since it is given that DEFG is an isosceles trapezoid, angles A and D are congruent. In other words, angle A = angle D.
Since angle A and angle D are opposite angles (meaning they are on opposite sides of the transversal AB), they are also congruent. Therefore, we can say that angle A = angle D = x degrees.
Now, let's find the measure of angle E.
Since angle E and angle F are supplementary (angle E + angle F = 180 degrees), we can substitute angle F with its value in terms of x.
angle F = 180 degrees - angle E (from the earlier equation)
Since angle F is opposite to angle D and they are congruent (angle D = x degrees), angle F must also be x degrees.
Therefore, we have:
x = 180 degrees - angle E
x = angle F
Now we can substitute x into the equation:
180 degrees - angle E = x
Substituting x with angle F:
180 degrees - angle E = angle F
Since angle F is congruent to angle E in an isosceles trapezoid, we can rewrite the equation:
180 degrees - angle E = angle E
Now we can solve for angle E:
180 degrees = 2 * angle E
Divide both sides by 2:
angle E = 90 degrees
So the measure of angle E in isosceles trapezoid DEFG is 90 degrees.