Question

# In the given figure:$$\angle b = 2a + 15^{\circ}$$ and $$\angle c = 3a + 5^{\circ}$$, find the value of $$\angle b$$.

A
100o
B
105o
C
95o
D
92o

Solution

## The correct option is B $$105^o$$Given the angles are:$${ a }, { 70 }^{ o }, b=2a+15^o$$ and $$c=3a+5^o$$.We know, by angle sum property, the sum of angles of a quadrilateral is $$360^o$$.$$a+b+c+70^o=360^o$$$$\Rightarrow a+2a+15^o+3a+5^o+70^o=360^o$$$$\Rightarrow 6a+90^o=360^o$$$$\Rightarrow 6a=270^o$$$$\Rightarrow a={ 45 }^{ o }$$.Therefore,$$\angle b=2a+15^o$$      $$=2(45^o)+15^o$$      $$=90^o+15^o$$      $$={ 105 }^{ o}$$Hence, option $$B$$ is correct.Mathematics

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