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Find the values of the angles x, y, and z in the given figure:

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∠

x = 45º,

∠

y = 45°,

∠

z = 100°

∠

x = 55º,

∠

y = 125°,

∠

z = 120°

∠

x = 45º,

∠

y = 90°,

∠

z = 140°

None of these

answer is B.

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Detailed Solution

Given figure is:
Question Image

Here, 55° and x are equal as they are vertically opposite angles.
This means that the value of x is 55°.
Now, since,

∠

y and 55° lie on the same line, so they are forming a linear pair which means that their sum is 180°.

\Rightarrow ∠ y + 55 ° = 180 °

\Rightarrow ∠ y = 180 ° - 55 °

\Rightarrow ∠ y = 125 °

Now, since

∠

y and

∠

z are vertically opposite angles, they are equal.

\Rightarrow ∠ y

∠

z
Therefore, the required angles are

∠

x = 55°,

∠

y = 125° and

∠

z = 125°.
Hence, option 2 is correct.

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