Question

5. In Fig. 6.32, if AB CD. APQ = 50° and
PRD=127°, find and y.​

Answer 1

Step-by-step explanation:

by linear pair

interior angle R = 180 - 127 = 53°

since AB is parallel to CD

by parallel lines theorem

exterior angle at P = 53°

angle y = 180 - (53+50) = 77°

since sum of ∆PQR is 180 °

angle x = 180 - (53 + 77) = 50°

Answer 2

Answer:

APQ = PQR (Alternate interior angles)

Now, putting the value of APQ = 50° and PQR = x we get,

x = 50°

Also,

APR = PRD (Alternate interior angles)

Or, APR = 127° (As it is given that PRD = 127°)

We know that

APR = APQ+QPR

Now, putting values of QPR = y and APR = 127° we get,

127° = 50°+ y

Or, y = 77°

Thus, the values of x and y are calculated as:

x = 50° and y = 77°