Explanation:
1.If the measure of angle D = 162° and angle C = 122°, then the sum of angles A, B, C, and D in the quadrilateral is 360 degrees. We can find the measures of angles A and B by subtracting the given angles from 360 degrees and dividing the result by 2.
A = (360 - 162 - 122) / 2 = 38 degrees B = (360 - 162 - 122) / 2 = 38 degrees
Therefore, the measure of angle A is 38 degrees and the measure of angle B is 38 degrees.
2.If the measure of angle D = 171° and angle C = 128°, then we can find the measures of angles A and B using the same method as above.
A = (360 - 171 - 128) / 2 = 30.5 degrees B = (360 - 171 - 128) / 2 = 30.5 degrees
Therefore, the measure of angle A is 30.5 degrees and the measure of angle B is 30.5 degrees.
3.If the measure of angle A = 22° and angle B = 35°, then the sum of angles A, B, C, and D in the quadrilateral is 360 degrees. We can find the measures of angles C and D by subtracting the given angles from 360 degrees and dividing the result by 2.
C = (360 - 22 - 35) / 2 = 151.5 degrees D = (360 - 22 - 35) / 2 = 151.5 degrees
Therefore, the measure of angle C is 151.5 degrees and the measure of angle D is 151.5 degrees.
4.If the measure of angle A = 20° and angle B = 29°, then we can find the measures of angles C and D using the same method as above.
C = (360 - 20 - 29) / 2 = 155.5 degrees D = (360 - 20 - 29) / 2 = 155.5 degrees
Therefore, the measure of angle C is 155.5 degrees and the measure of angle D is 155.5 degrees