Final answer:
To solve the problem, set up an algebraic equation considering the sum of angles in a quadrilateral is 360 degrees. Given that two adjacent angles are equal and one is 90 degrees, the quadrilateral ends up being a rectangle, with each of the four angles measuring 90 degrees.
Step-by-step explanation:
The question asks us to find the measure of each angle in a quadrilateral with a pair of adjacent angles that are equal, and one angle that is 90 degrees. In a quadrilateral, the sum of all the angles is 360 degrees. Since one angle is 90 degrees and the pairs of adjacent angles are equal, we can denote the two equal angles as x.
The fourth angle will also be 90 degrees because the pairs of angles are adjacent and equal. So we have two equal angles (x + x) and two 90-degree angles (90 + 90), adding up to 360 degrees.
Using an algebraic equation:
90 + 90 + x + x = 360
180 + 2x = 360
2x = 180
x = 90
Thus, each of the equal adjacent angles measures 90 degrees as well, making the quadrilateral a rectangle. This means that all four angles of the quadrilateral are 90 degrees each.