Final answer:
To find the measures of angles mza and mzabc in the trapezoid ABCD, we can use the properties of parallel lines and the properties of angles in a trapezoid.
Step-by-step explanation:
To find the measures of angles mza and mzabc in the trapezoid ABCD, we can use the properties of parallel lines and the properties of angles in a trapezoid.
Angle mza is vertically opposite to angle mzabc. Therefore, they have the same measure.
Since AB is parallel to CD, angle mza and angle mzabc are corresponding angles. So, they have the same measure. To find their measure, we need to find the measure of angle ABC.
Since AB is parallel to CD, angle ABC and angle CDA are corresponding angles. Therefore, they have the same measure. We can use the property of angles in a trapezoid: the sum of the measures of the base angles is equal to 180 degrees. In this case, angle ABC and angle CDA are the base angles.
Let's solve for angle ABC:
angle ABC + angle CDA = 180 degrees
angle ABC + angle ABC = 180 degrees (angle CDA and angle ABC have the same measure)
2 * angle ABC = 180 degrees
angle ABC = 90 degrees
Since angle mza and angle mzabc are corresponding angles, they have the same measure. Therefore, angle mza = angle mzabc = 90 degrees.