In the given figure, if the lines l1 and l2 are parallel to each other, and the transversal line m intersects it. What is the value of y?a)52b)78c)128d)138e)168Correct answer is option 'C'. Can you explain this answer?

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In the given figure, if the lines l₁ and l₂ are parallel to each other, and the transversal line m intersects it. What is the value of y?

a)
52°
b)
78°
c)
128°
d)
138°
e)
168°

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

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In the given figure, if the lines l1 and l2 are parallel to each other...

Step 1: Question statement and Inferences

We are given that two parallel lines l₁ and l₂ are intersected by a transversal line m. Also, the angles formed are shown as 2x, 3x + 50, a, b, and y.

We have to find the value of angle y.

Now, to find the value of y, we need to establish the relation between x and y. Since the lines l₁ and l₂ are parallel lines and the transversal line m intersects them,

2x = a (Corresponding angles)

Also, since

a = b (Vertically opposite angles)

Hence,

b = 2x

Also,

(3x + 50) + a = 180º

(3x + 50) + 2x = 180º

5x + 50 = 180º

5x = 130º

x = 26º ……………………… (1)

Step 2: Finding required values

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

a + b + (3x + 50) + y = 360º

Thus,

2x + 2x + y + y = 360º

7x + y + 50 = 360º

7x + y = 310º …… (2)

By putting the value of x from equation (1) to equation (2), we get:

7*26 + y = 310º

182 + y = 310º

y = 128º

Step 3: Calculating the final answer

So, the value of y = 128º

Answer: Option (C)

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In the given figure, if the lines l1 and l2 are parallel to each other, and the transversal line m intersects it. What is the value of y?a)52°b)78°c)128°d)138°e)168°Correct answer is option 'C'. Can you explain this answer?

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