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In the figure given below, if the three lines AB, CD, and EF are coplanar intersecting at O, then what are the measures of the angles $x, y, z, and u$ ?

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

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

x = 40 °, u = 40 °, y = 60 °, and z = 90 °

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

answer is A.

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Detailed Solution

It is given that the three lines AB, CD, and EF are coplanar intersecting at O.
Using the linear pair property, we have,

∠ E O D + ∠ D O F = 180 ° ⇒ ∠ E O P + ∠ B O D + ∠ D O F = 180 °

⇒ x + 90 ° + 50 ° = 180 ° ⇒ x = 40 °

Using the vertically opposite angles property, we have,

x = u = 40 °

y = 50 ° z = 90 °

Therefore, the measures of the angles are

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

Hence, option (1) is correct.

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