Given: abcd is a trapezoid, ab=cd, mn is a midsegment, mn=30, bc=17, ab=26 find: m∠a, m∠b, m∠c, and m∠d

m∠A=m∠D=60°, m∠B=m∠C=120°

Step-by-step explanation:

Consider isosceles trapezoid ABCD with midsegment MN. Draw two trapezoid heights BF and CE. Then quadrilateral FBCE is rectangle and EF=BC=17 units.

By the trapezoid midsegment theorem,

Segments FA and ED are equal to

In right triangle ABF, the hypotenuse AB is twice greater than the leg FA, then m∠FBA=30°.

m∠B=m∠FBA+m∠CBF=30°+90°=120°.

In isosceles trapezoid

m∠B=m∠C=120°,

m∠A=m∠D and m∠A=180°-m∠B=180°-120°=60°=m∠D.

answer: 177/8

step-by-step explanation: