Question

In a trapezoid ABCD, AB = DC and BK is the altitude. If AB = 8 and AK = 4, find the measure of angle A and the measure of angle ABC.

Answer 1

To find the measure of angle A, use the Pythagorean theorem and the tangent formula. Angle ABC can be found using the fact that angles on a straight line add up to 180 degrees.

Step-by-step explanation:

In a trapezoid, the measure of an angle can be found using the properties of parallel lines and alternate interior angles. In this case, we can use the fact that AB = DC to determine the measure of angle A. Since AB = 8 and AK = 4, we can apply the Pythagorean theorem to find BK. Using the formula for the tangent of an angle, we can find the measure of angle A. To find angle ABC, we can use the fact that angles on a straight line add up to 180 degrees. We know that angle A is equal to angle C, so angle ABC is equal to 180 - 2(angle A).