Question

In the given figure
PqllRs. Find the value
of x
​

Answer 1

Answer: 83°

Step-by-step explanation: Draw a line from S to Q. This line is also a transversal. So we can say tha ∠S+∠Q = 180° Angle sum of a pentagon

is 540. ∴ 180+135+142+x = 540

                 540-457 = x

                 x = 83°

Answer 2

Answer:

x = 83 degree

Step-by-step explanation:

GIVEN : PQ // RS

             Angle P = 135

             Angle R = 142

TO FIND : x

CONSTRUCTION: draw a line parallel to PQ & RS and lies between PQ &

                                                                                                                  RS

PROOF:

As we if 2 lines are parallel then there alternate interior angles are equal

Therefore ,

Angle 3 = PQ = 135

Angle 4 = RS = 142

Also ,

Angle 3 + Angle 1 = 180                  (linear pair)

Angle 1 + 135 = 180

Angle 1 = 180 - 135 = 45

Similarly ,

Angle 4 + Angle 2 = 180                  (linear pair)

Angle 2 + 142 = 180

Angle 2 = 180 - 142 = 38

Angle x  = Angle 1 + Angle 2

              = 45 + 38

               = 83