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Question

In a triangle $$ABC ,$$ the measure of  $$\angle A$$ is  $$40 ^ { \circ }$$  less then the measure of $$\angle B$$ is $$50 ^ { \circ }$$  less than  that  $$\angle C .$$ Find the measure of   $$\angle A$$


Solution

$$\begin{array}{l} Let\, the\, measure\, \, of\, \angle C\, be\, { x^{ \circ  } } \\ measure\, of\, \angle B=x-{ 50^{ \circ  } } \\ measure\, \, of\, \angle =x-{ 90^{ \circ  } } \\ a/q \\ 3x-{ 140^{ \circ  } }={ 180^{ \circ  } } \\ x=60+\frac { { 140 } }{ 3 }  \\ measure\, of\, \angle A=\frac { { 140 } }{ 3 } -30 \\ =\frac { { { { 50 }^{ \circ  } } } }{ 3 } . \end{array}$$

Mathematics

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