Question

Quadrilateral ABCD is congruent to quadrilateral EFGH . Angle A is a right angle, the measure of angle E is (y^2−10)degrees and the measure of angle H is (2y^2−132)degrees. Find the measure of angle D.

Answer 1

Answer: 28 degrees

Explanation

angle A = angle E because the corresponding pieces are congruent.

Notice that A and E are the first letters mentioned of ABCD and EFGH respectively.

Because of this, we form the equation y^2-10 = 90 which leads to y^2 = 80.

We don't need to isolate y itself.

angle H = 2y^2 - 132 = 2*80-132 = 28 degrees which is also the measure of angle D.

Notice that D and H are the last letters mentioned of ABCD and EFGH respectively.

Answer 2

Angle D is a right angle with a measure of 90 degrees because quadrilateral ABCD is congruent to quadrilateral EFGH and has a right angle at angle A.

Step-by-step explanation:

The student's question involves finding the measure of angle D in a congruent quadrilateral given that angle A is a right angle and there are algebraic expressions for the measures of angles E and H. Since ABCD is congruent to EFGH, they have corresponding angles of equal measures. Since angle A is a right angle, and ABCD and EFGH are congruent, angle D is also a right angle and measures 90 degrees.