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Offline Centres

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

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∠

x = 45º,

∠

y = 40°,

∠

z = 140°

∠

x = 115º,

∠

y = 125°,

∠

z = 140°

∠

x = 115º,

∠

y = 140°,

∠

z = 40°

None of these

answer is C.

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Detailed Solution

Given figure is:
Question Image

Here, 40°, x and 25° are forming a linear pair.

\Rightarrow 40 ° + x + 25 ° = 180 °

\Rightarrow x + 65 ° = 180 °

\Rightarrow x = 180 ° - 65 °

\Rightarrow x = 115 °

This means that the value of x is 115°.
Similarly, since,

∠

y and 40° lie on the same line, so, they are forming a linear pair which means that their sum is 180°.

\Rightarrow ∠ y + 40 ° = 180 °

\Rightarrow ∠ y = 180 ° - 40 °

\Rightarrow ∠ y = 140 °

Now, again

∠

y and

∠

z are forming linear pairs,

\Rightarrow ∠ y + ∠ z = 180 °

\Rightarrow ∠ z = 180 ° - 140 °

\Rightarrow ∠ z = 40 °

Therefore, the required angles are

∠

x = 115°,

∠

y = 140° and

∠

z = 40°.
Hence, option 3 is correct.

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