In figure BP bisects ∠ABC and AB=AC. Find x

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27.2

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answer is A.

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Detailed Solution

In triangle ABC the side AB=AC
Now since we know that the angles opposite to equal sides are equal, hence we can say ⇒∠ABC=∠ACB
Let us assume that ∠ABC=∠ACB=k
Now since we know that the sum of internal angles of a triangle is equal to 180 degree, Hence,
⇒∠ABC+∠ACB+∠BAC=180
⇒k+k+60∘=180∘
⇒2k=180∘−60∘

\Rightarrow k = \frac{120 °}{2}

⇒k=60∘
∴∠ABC=∠ACB=60∘
Now since the line BP is the angle bisector of the ∠ABC, so ∠ABP=∠PBC
Hence,

\Rightarrow ∠ ABP = ∠ PBC = \frac{∠ ABP}{2} = 30 \circ

We can see that the line AP is parallel to the line BC so by using the alternate interior angle theorem we can say
⇒∠PBC=∠BPA
Hence we can say
⇒∠PBC=∠BPA=30∘
Therefore, x=30∘
So, the correct answer is “ x = 30∘”.

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