Quadrilateral PQRS is a rectangle with diagonals PR and QS. If the measure of angle 1 = 18, find the measures of angles 2, 3, and 4. Explain how to get the answer please. Thanks in advance!
triangle RST is an isoselese triangle so angle 1 = angle 2
so angle 2 = 18
since we have a rectangle, angle 2 + angle 3 = 90
=> angle 3 = 90 - 18 = 72
again, triangle TQR is isoselese, so angle 4 = angle 3 = 72 but we could have found it otherwise. consider the triangle QRS. the angles in a triangle add up to 180. so we have:
angle 1 + (angle 2 + angle 3) + angle 4 = 180 .....we should count angle 2 and 3 as one angle, so i put it in brackets
=> 18 + 90 + angle 4 = 180
=> angle 4 = 180 - 18 - 90 = 72