The above figure is a special trapezoid. explain the relationship between the m∠b and m∠c.

They are supplementary

Step-by-step explanation:

Since AB and DC are parallel, then the alternate interior angles are congruent because there is transversal cutting the parallel lines (BC). So m<B is supplementary to m<C

As we already know that, in a trapezoid there is two parallel sides.

So, these angles must be supplementary.

Therefore, m∠B + m∠C = 180°.

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.