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Question

In the given figure:
$$\angle b = 2a + 15^{\circ}$$ and $$\angle c = 3a + 5^{\circ}$$, find the value of $$\angle b $$.
179890.jpg


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