If the lines l1 and l2 are parallel to each other, and the transversal line m intersects it such thatPRS= 3a andRYX= 6b, then what is the value of a + 2b ?a)30b)60c)80d)90e)120Correct answer is option 'B'. Can you explain this answer?

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If the lines l₁ and l₂ are parallel to each other, and the transversal line m intersects it such that ∠PRS= 3a and ∠RYX= 6b, then what is the value of “a + 2b” ?

a)
30°
b)
60°
c)
80°
d)
90°
e)
120°

Correct answer is option 'B'. Can you explain this answer?

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If the lines l1 and l2 are parallel to each other, and the transversal...

Step 1: Question statement and Inferences

We are given that two parallel lines l₁ and l₂ are intersected by a transversal line m. Also, two angles 3a and 6b are formed as shown in the figure.

We have to find the value of "a + 2b".

We know that,

∠RYX=∠PRQ (Corresponding angles) So, ∠PRQ = 6b……………(1) Also,

∠PRS = ∠QRY=3a (Vertically opposite angles)

And ,

∠PRQ = ∠SRY= 6b (Vertically opposite angles)

Step 2: Finding required values

Now, we know that the sum of all the angles formed around a point is 360^o. So,

∠PRS + ∠SRY + ∠QRY + ∠PRQ=360^∘

Thus,

3a + 6b + 3a + 6b =360^∘

6a+12b=360^∘

a+2b=60^∘

Step 3: Calculating the final answer

So, the sum a + 2b = 60

Answer: Option (B)

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If the lines l1 and l2 are parallel to each other, and the transversal line m intersects it such that∠PRS= 3a and∠RYX= 6b, then what is the value of “a + 2b” ?a)30°b)60°c)80°d)90°e)120°Correct answer is option 'B'. Can you explain this answer?

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