Final answer:
In a trapezoid ABCD, with AB=DC and BK as the altitude, the measures of angle A and angle ABC are 90°.
Step-by-step explanation:
In a trapezoid ABCD, where AB=DC, if BK is the altitude and AB=8 and AK=4, we can solve for the measures of angle A and angle ABC.
Step 1: Recognize that since AB=DC, opposite sides of a trapezoid are parallel.
Step 2: Since BK is the altitude, angle A is a right angle, or 90°.
Step 3: To find angle ABC, use the property that opposite angles in a trapezoid are congruent. Since angle A is 90°, angle ABC is also 90°.
Therefore, m∠a = 90° and m∠abc = 90°.