Trapezoid A B C D is shown. A diagonal is drawn from point B to point D. Sides B C and A D are parallel. Sides B A and C D are congruent. Angle C B D is 24 degrees and angle B A D is 116 degrees. What is the measure of angle ABD in trapezoid ABCD? 24° 40° 64° 92

40 degrees

Step-by-step explanation:

The given trapezoid ABCD is shown in the figure, in which sides BC and AD are parallel.

Angle CBD=24 degrees.

Angle BAD=116 degrees.

As the diagonal BD cuts the two parallel sides BC and AD, so

Angle CBD = Angle ADB [alternate angles]

So, Angle ADB= 24 degrees.

Now, in the triangle ABD, the sum of all the three angles,

Angle ABD + Angle ADB + Angle BAD =180 degrees.

Angle ABD + 24 degrees + 116 degrees =180 degrees

So, Angle ABD= 180 - 24 - 116= 40 degrees.

Hence, Angle ABD = 40 degrees.