Question
Find the values of the unknown interior angle in the following figures.
✓
Answer
(i) $\because$ Exterior angle $=110^{\circ}$
One of the interior opposite angle $=40^{\circ}$
By exterior angle property of triangle,
$x+40^{\circ}=110^{\circ} $
$\Rightarrow \quad x=110^{\circ}-40^{\circ}=70^{\circ}$
(ii) $\because$ Exterior angle $=130^{\circ}$
One of the interior opposite angle $=45^{\circ}$
By exterior angle property of triangle,
$130^{\circ} =45^{\circ}+x $
$\Rightarrow \quad x =130^{\circ}-45^{\circ}=85^{\circ}$
One of the interior opposite angle $=40^{\circ}$
By exterior angle property of triangle,
$x+40^{\circ}=110^{\circ} $
$\Rightarrow \quad x=110^{\circ}-40^{\circ}=70^{\circ}$
(ii) $\because$ Exterior angle $=130^{\circ}$
One of the interior opposite angle $=45^{\circ}$
By exterior angle property of triangle,
$130^{\circ} =45^{\circ}+x $
$\Rightarrow \quad x =130^{\circ}-45^{\circ}=85^{\circ}$
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