CTET 2 Math and Science Sep 2014 Paper

Question : 49 of 120

Marks: +1, -0

If one angle of a triangle is 130°, then the angle between the bisectors of the other two angles is

Solution:

We know that

∠{A}+∠{B}+∠{C}=180^{∘}

130^{∘}+∠{B}+∠{C}=180^{∘}

∠{B}+∠{C}=180^{∘}-130^{∘}=50^{∘}

Dividing both sides by 2

\;\;{∠{C}+∠{B}}/{2}=\;\;{50}/{2}=25

Now ΔBOC

\;\;{∠{C}}/{2}+\;\;{∠{B}}/{2}+∠{BOC}=180^{∘}

∴∠{C}=180^{∘}-(\;\;{∠{B}+∠{C}}/{2})

=180^{∘}-25^{∘}=155^{∘}

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