Question : One angle of an isosceles obtuse triangle is $28 \frac{1}{2}^{\circ}$. Find the measure of its obtuse angle in degrees.
Option 1: $132^{\circ}$
Option 2: $112^{\circ}$
Option 3: $121^{\circ}$
Option 4: $123^{\circ}$
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Correct Answer: $123^{\circ}$
Solution :
One of the angles of obtuse-angled isosceles triangle is $\frac{57}{2}^\circ$, the other same angle will be $\frac{57}{2}^\circ$.
Let the obtuse angle be $x$.
Thus, the sum of angles of a triangle $=180^\circ$
⇒ $\frac{57}{2}+\frac{57}{2}+x=180^\circ$
⇒ $\frac{114}{2}+x=180^\circ$
⇒ $57+x=180^\circ$
⇒ $x=123^\circ$
So, the measure of its obtuse angle is $123^\circ$.
Hence, the correct answer is $123^\circ$.
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