Question
An exterior angle of a triangle is 105º and its two interior opposite angles are equal. Each of these equal angles is:
✓
Answer
- $52\frac{1}{2}^\circ$
Solution:
Let one of interior angle be xº
Sum of two opposite interior angles = Exterior angle
$\therefore$ xº + xº = 105º [ $\therefore$ Exterior angle = 105º (given)]
$\Rightarrow2\text{x}^\circ=105^\circ$
$\therefore\text{x}^\circ=\frac{105^\circ}{2}$
$\Rightarrow\text{x}^\circ=52\frac{1}{2}$
Hence, each angle of a triangle is $52\frac{1}{2}^\circ.$
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