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In the given figure, three coplanar lines intersect at a point O, forming angles as shown in the figure. Find the values of x, y, z and u.

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∠ x = 40 °, ∠ y = 30 °, ∠ z = 80 ° and ∠ u = 50 °

∠ x = 40 °, ∠ y = 50 °, ∠ z = 90 ° and ∠ u = 40 °

∠ x = 40 °, ∠ y = 50 °, ∠ z = 70 ° and ∠ u = 70 °

∠ x =

30 °, ∠ y = 70 °, ∠ z = 70 ° and ∠ u = 60 °

answer is B.

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Detailed Solution

It is given that three coplanar lines intersect at a point O, forming angles as shown in the figure.
The vertically opposite angles are equal.
We can observe from the figure that the angles AOF, FOD and DOB are linear pairs,
Question Image

So, we can write that,

⇒ 900 + 500 + u 0 = 1800

(Linear pair)

⇒ u 0 + 1400 = 1800

⇒ u 0 = 1800 − 1400

⇒ u 0 = 400

We can also observe from the figure that,

x 0

and

u 0

are vertically opposite.
Hence, we can write that,

⇒ x 0 = u 0 = 400

(Vertically Opposite angle).
We can also observe that

z 0

is vertically opposite to angle DOB.

⇒ z 0 = 90

(Vertically Opposite angle).
We can also see that angles AOC, COE and EOB are linear pairs of angles.

⇒ z 0 + y 0 + x 0 = 1800

(Linear pair)
Apply values.

⇒ 900 + y 0 + 400 = 1800

⇒ y 0 + 1300 = 1800

⇒ y 0 = 1800 − 1300

⇒ y 0 = 500

The angles x, y, z and

u

are

400, 500, 900

and

400

respectively.
Hence, the correct option is 2.

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