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in Constructions by (36.7k points)
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If in ΔABC \(\overrightarrow{BX}\) and \(\overrightarrow{CX}\) are bisectors to the base angles then ∠BXC = 

A) 90° + 1/2∠A 

B) 90° – 1/2∠A 

C) 180°- 1/2∠A 

D) None

2 Answers

+1 vote
by (57.0k points)
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Best answer

Correct option is (A) 90° + 1/2 ∠A

\(\angle A+\angle B+\angle C\) \(=180^\circ\)     (Sum of angles in \(\triangle ABC)\)

\(\Rightarrow\) \(\frac{\angle A}2+\frac{\angle B}2+\frac{\angle C}2\) \(=\frac{180^\circ}2\)

\(\Rightarrow\) \(\frac{\angle B}2+\frac{\angle C}2\) \(=90^\circ-\frac{\angle A}2\)

\(\Rightarrow\) \(\angle XBC+\angle XCB=90^\circ-\frac{\angle A}2\)

\((\because\) BX and CX are angle bisectors of \(\angle B\;\&\;\angle C)\)

\(\therefore\) \(\angle BXC\) \(=180^\circ-(\angle XBC+\angle XCB)\)

\(=180^\circ-(90^\circ-\frac{\angle A}2)\)

\(90^\circ+\frac{\angle A}{2}\)

+1 vote
by (38.9k points)

A) 90° + 1/2∠A 

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