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Question

In the given figure $$\triangle ABC$$ side $$AC$$ has been produced to $$D$$. $$\angle BCD = 125^o$$ and $$\angle A : \angle B = 2 : 3$$, find the measure of $$\angle A$$ and $$\angle B$$.
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Solution

Let  $$\angle A=2x$$ and $$\angle B=3x$$
$$\angle BCD=\angle B+\angle A$$ (Sum of exterior angle of triangle is equal to sum of two opposite interior angles )
$$2x+3x={ 125 }^{ \circ  }\\ 5x={ 125 }^{ \circ  }\\ x=\dfrac { { 125 }^{ \circ  } }{ 5 } ={ 25 }^{ \circ  }\\ \angle A=2x=2\times { 25 }^{ \circ  }=50^{ \circ  }\\ \angle B=3\times { 25 }^{ \circ  }={ 75 }^{ \circ  }$$


Mathematics

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