Iven: 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

Step-by-step explanation:

ABCD is isosceles trapezoid, because AB=CD.

1. The midsegment MN=30, the smaller base BC=17, thenyou can find the greater base:

2. Draw two trapezoid's heights BH and CK. Triangles ABH and CDK are congruent and

3. In right triangle ABH, the hypotenuse AB=26 and the leg AH=13, then angle opposite to the leg AH is 30°. This means that

Thus,

m∠A=60°, m∠B=120°, m∠C=120°, and m∠D=60°

Step-by-step explanation:

Given: ABCD is a trapezoid, AB=CD, MN is a mid-segment

where, MN=30, BC=17, AB=26.

Using given info, draw trapezoid. Please see attachment for figure.

ABCD is isosceles trapezoid.  (∵ AB=CD)

The length of mid-segment is equal to average of two parallel side of trapezoid.

Draw two perpendicular from B and C at F and E respectively on AD. Such that ΔABF≅ΔDCE

Therefore, FA=DE by CPCT

2FA=AD-BC

2FA=43-17

2FA=26

FA=13

In ΔAEB, ∠E=90°

Therefore, ∠A=60°

It is isosceles trapezoid.

Therefore, ∠A=∠D=60°

∠A+∠B=180° (Sum of angles between two parallel line on same side of transversal line is 180°)

∠B=180-60=120°

∠B=∠C=120°

Thus, m∠A=60°, m∠B=120°, m∠C=120°, and m∠D=60°

25

step-by-step explanation: