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Thepotemich [5.8K]

3 years ago

14

“If the alternate exterior angles are congruent, then the lines are parallel.”

1 answer:

sergeinik [125]3 years ago

5 0

The correct answer is <span>If the alternate exterior angles are not congruent, then the lines are not parallel.

The inverse one is the one with the nots in it. Although the fourth version also has nots, it is actually a contrapositive because of the virtue of its form. </span>

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

Elis [28]

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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3 years ago

Which equation is equivalent to n+4 = 11?

WITCHER [35]

Answer:

n = 7

Step-by-step explanation:

n+ 4 = 11 subtract 4 from both sides of the equation

n + 4 -4 = 11-4

n = 7

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