Question

In the diagram, PQRS, JQK and LRK are straight lines what is the size of the angle JKL?

Answer 1

Given : PQRS, JQK and LRK are straight lines  

To find : size of the angle JKL?

Solution:

PQR is Straight line

=> 2y  + x  +  ∠MQR   = 180°

SRQ is Straight line

=> 2x + y + ∠MRQ    = 180°

Adding both => 3x  + 3y  + ∠MQR  + ∠MRQ = 360°

∠MQR  + ∠MRQ + 33° = 180°

=>  ∠MQR  + ∠MRQ  =  147°

=>  3x  + 3y  +  147°  = 360°

=> 3x + 3y  = 213°

=> x + y  = 71°

x     +  ∠MQR   =  ∠QRK  + ∠QKR

y +   ∠MRQ = ∠KRQ  + ∠QKR

=> x + y +  ∠MQR + ∠MRQ =  ∠QRK + ∠QKR  + ∠KRQ  + ∠QKR

=> 71° + 147°  = 180° + ∠QKR

=> ∠QKR = 38°

∠QKR  = ∠JKL

=> ∠JKL  = 38°

∠JKL  = 38°  

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Answer 2

Answer:

38

Step-by-step explanation:

2x=2y

So, x=y

2x+y = 33+180-2y-x (Exterior angle = sum of opposite interior angles)

2x+y=213-2y-x

3x+3y=213

3(x+y)=71

x+y=71

Basically,

2x=71 (Because x=y as defined above)

opposite angles are equal.

So, 71+71+JKL=180

142+JKL=180

JKL=38