Question

DEFG is an isosceles trapezoid. Find the measure of E.

Answer 1

If it is isosceles angle E must be equal to F, in this case 75°

Answer 2

Answer:  The measure of ∠E is 75°.

Step-by-step explanation: Given that DEFG is an isosceles trapezoid, where m∠D = 105° and m∠F = 75°.

We are to find the measure of ∠E.

ISOSCELES TRAPEZOID is a trapezoid in which the base angles are equal and so the left and right side lengths are also equal.

Therefore, in the isosceles trapezoid DEFG, we have

m∠D = m∠G,  m∠E = m∠F  and  DE = FG.

Since, m∠D = 105°, so m∠G =  105°.

The sum of all the four angles of a quadrilateral is 360° and a trapezoid is a quadrilateral with a set of opposite parallel sides, so in the trapezoid DEFG, we have

$m\angle D+m\angle E+m\angle F+m\ange G=360^\circ\\\\\Rightarrow 105^\circ+m\angle E+75^\circ+105^\circ=360^\circ\\\\\Rightarrow m\angle E+285^\circ=360^\circ\\\\\Rightarrow m\angle E=360^\circ-285^\circ\\\\\Rightarrow m\angle E=75^\circ.$

Thus, the measure of ∠E is 75°.