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