Question
Find the unknown marked angles in the given figure:
✓
Answer
We know that in a triangle if one side of it is produced, then
Exterior angle $=$ sum of its interior opposite angles.
In fig.,
$105^{\circ}=b+b$
$\Rightarrow 2 \mathrm{~b}=105^{\circ}$
$\Rightarrow \mathrm{b}=\frac{105^{\circ}}{2}=52.5^{\circ}$
But a $+105^{\circ}=180^{\circ}$ .. (Linear pair)
$\Rightarrow \mathrm{a}=180^{\circ}-105^{\circ}=75^{\circ}$
Hence $a=75^{\circ}, b=52.5^{\circ}$
Exterior angle $=$ sum of its interior opposite angles.
In fig.,
$105^{\circ}=b+b$
$\Rightarrow 2 \mathrm{~b}=105^{\circ}$
$\Rightarrow \mathrm{b}=\frac{105^{\circ}}{2}=52.5^{\circ}$
But a $+105^{\circ}=180^{\circ}$ .. (Linear pair)
$\Rightarrow \mathrm{a}=180^{\circ}-105^{\circ}=75^{\circ}$
Hence $a=75^{\circ}, b=52.5^{\circ}$
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