Question

What is the answer to this question? In the diagram, PQRS, JQK and LRK are straight lines what is the size of the angle JKL?

Answer 1

Answer:

Step-by-step explanation:

y + 2x + ∠MRQ = 180 (straight line PQRS)

∠MRQ = 180- y - 2x

2y + x + ∠MQR = 180  (straight line PQRS)

∠MQR = 180 - 2y -x

∠MRQ + ∠MQR  + 33 = 180 (Sum of angles of triangle)

180- y - 2x + 180 - 2y -x + 33 = 180

-3y-3x = 180-180-180-33

3(y+x) = 213

y+x = 71.

∠QRK = 2x (Vertically opposite angle)

∠KQR = 2y  (Vertically opposite angle)

∠QRK+∠KQR + ∠JKL = 180  (Sum of angles of triangle)

2x + 2y + ∠JKL = 180

∠JKL = 180 - 2(x+y)

∠JKL = 180 - 2×71

∠JKL = 180 - 142

∠JKL = 38°