MCQ
An exterior angle of a triangle is $105^\circ $ and its two interior opposite angles are equal. Each of these equal angles is:
- A$37\frac{1}{2}^\circ$
- ✓$52\frac{1}{2}^\circ$
- C$75^\circ$
- D$72\frac{1}{2}^\circ$
✓
Answer
Correct option: B.
$52\frac{1}{2}^\circ$
Let one of interior angle be $x^\circ $
Sum of two opposite interior angles = Exterior angle
$\therefore x^\circ + x^\circ = 105^\circ $ [ $\therefore$ Exterior angle $= 105^\circ$ (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 $52\frac{1}{2}^\circ.$
Sum of two opposite interior angles = Exterior angle
$\therefore x^\circ + x^\circ = 105^\circ $ [ $\therefore$ Exterior angle $= 105^\circ$ (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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