Mathematics

In the figure above, what is the ratio of the measure of angle B to the measure of angle A?


ANSWER

4 to 5


SOLUTION
Using angle sum property 
$$\angle A+\angle B+\angle C={ 180 }^{ \circ  }\\ \Rightarrow { (y+10) }^{ \circ  }+{ y }^{ \circ  }+{ 90 }^{ \circ  }={ 180 }^{ \circ  }\\ \Rightarrow 2y={ 180 }^{ \circ  }-{ 100 }^{ \circ  }\\ \Rightarrow y={ 40 }^{ \circ  }$$
So the angles are
$$\angle A=y+{ 10 }^{ \circ  }={ 50 }^{ \circ  }\\ \angle B=y={ 40 }^{ \circ  }\\ \Rightarrow \angle B:\angle A=4:5$$
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