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Brut [27]
3 years ago
13

Given: ABCD trapezoid, BK ⊥ AD , AB=DC AB=8, AK=4 Find: m∠A, m∠B

Mathematics
1 answer:
Elis [28]3 years ago
7 0

Answer:

m\angle B=m\angle C=120^{\circ}

m\angle A=m\angle D=60^{\circ}

Step-by-step explanation:

Trapezoid ABCD is isosceles trapezoid, because AB = CD (given). In isosceles trapezoid, angles adjacent to the bases are congruent, then

  • \angle A\cong \angle D;
  • \angle B\cong \angle C.

Since BK ⊥ AD, the triangle ABK is right triangle. In this triangle,  AB = 8, AK = 4. Note that the hypotenuse AB is twice the leg AK:

AB=2AK.

If in the right triangle the hypotenuse is twice the leg, then the angle opposite to this leg is 30°, so,

m\angle ABK=30^{\circ}

Since BK ⊥ AD, then BK ⊥ BC and

m\angle KBC=90^{\circ}

Thus,

m\angle B=30^{\circ}+90^{\circ}=120^{\circ}\\ \\m\angle B=m\angle C=120^{\circ}

Now,

m\angle A=m\angle D=180^{\circ}-120^{\circ}=60^{\circ}

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