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$∠ X$ and $∠ Y$ are exterior angles of $Δ A B C$ at the points $B$ and $C$ respectively. Also $∠ B > ∠ C,$ then the relation between $∠ X$ and $∠ Y$ is:

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∠ X > ∠ Y

∠ X < ∠ Y

∠ X = ∠ Y

∠ X ≥ ∠ Y

answer is B.

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Detailed Solution

Given that

∠ X

and

∠ Y

are exterior angles of

Δ A B C

at the points B and C.
Also,

∠ B > ∠ C

Now, by using exterior angle theorem, we get,

∠ X = ∠ A + ∠ C

Again, by using exterior angle theorem, we get,

∠ Y = ∠ A + ∠ B

So,

∠ B > ∠ C

\Rightarrow

∠ Y − ∠ A > ∠ X − ∠ A

∴ ∠ Y > ∠ X

So, if

∠ X

and

∠ Y

are exterior angles of

Δ A B C

with respect to B and C, also

∠ B > ∠ C

, then

∠ X < ∠ Y

.
Hence, the correct option is 2.

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