Mathematics

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

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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