In the figure above, quadrilateral ABCD is a parallelogram. Let x represent the measure of angle GBF, y represent the measure of angle CBE, and z represent the measure of angle BCE. The value of x is °, the value of y is °, and the value of z is °.
Accepted Solution
A:
Answers: measure angle x = 40° measure angle y = 35° measure angle z = 55°
Explanation: Part (a): getting angle x: In triangle BED, we have: measure angle BED = 90° measure angle BDE = 50° Therefore: measure angle DBE = 180 - (90+50) = 40° Now, we have angle DBE and angle GBF vertically opposite angles.This means that they are both equal. Therefore angle GBF = 40° Since angle GBF is x, therefore: x = 40°
Part (b): getting angle y: We know that the sum of measures of angles on a straight line is 180.This means that: angle GBF + angle GBC + angle CBE = 180 We have:angle GBF = 40° angle GBC = 105° angle CBE = y Therefore: 40 + 105 + y = 180 y = 35°
Part (c): getting angle z: In triangle BCE, we have: measure angle BCE = z measure angle BEC = 90° measure angle CBE = 35° Therefore:z + 90 + 35 = 180 z = 55°