Question

In the adjoining figure side ab of parallelogram ABCD has been produced to E . If angle CBE = 75°, find the measure of each angle of parallelogram​

Answer 1

Answer:

The each angle of parallelogram are_

angleA = 75

angleB = 105

angleC = 75

angleD = 105

Step-by-step explanation:

Given- ABCD is a parallelogram

angleCBE = 75

To find- each angle of parallelogram

i.e. angle A,B,C and D

Solution- As AE is straight line and angle CBE and CBA are linear pair of angle

therefore, CBE + CBA = 180 ( sum of linear pair of angle is 180)

75 + CBA = 180

CBA = 180-75

CBA = 105

i.e. angleB is 105

since, ABCD is a parallelogram

therefore, all the opposite angle are equal

B = D = 105 (eq.1)

and A = C = x (eq.2)

since, parallelogram is a quadrilateral

therefore, sum of all the angle is 360

= A + B + C + D = 360

= x + 105 + x + 105 = 360 (from eq 1 and 2)

= 2x + 210 = 360

= 2x = 360 - 210

= x = 150/2

= x = 75

therefore, angle A and C is 75

Hence, angle A = 75

B = 105

C = 75

D = 105