Question

In a triangle, the smallest angle is 25° more than one-fourth of the greatest angle. If the third angle is 10° more than the smallest, then the sum of the smallest and the greatest angle is

• A. 100°
• B. 135°
• C. 125°
• D. 180°

Answer 1

The correct option is C 125°

Let the greatest angle be x.
∴ Smallest angle $=\frac{x}{4}+{25}^{\circ }$
and, the third angle $={10}^{\circ }+(\frac{x}{4}+{25}^{\circ })$
$={35}^{\circ }+\frac{x}{4}$
By Angle sum property, the sum of all the three angles in a triangle is 180°.
$\therefore x+(\frac{x}{4}+{25}^{\circ })+(\frac{x}{4}+{35}^{\circ })={180}^{\circ }$
$\Rightarrow \frac{3x}{2}+{60}^{\circ }={180}^{\circ }$
$\Rightarrow \frac{3x}{2}={120}^{\circ }$
$\Rightarrow x=\frac{2}{3}\times {120}^{\circ }={80}^{\circ }$
∴ Greatest angle = 80°
And, the smallest angle = $\frac{{80}^{\circ }}{4}+{25}^{\circ }={45}^{\circ }$
∴ Required sum = 80° + 45°
= 125°
Hence, the correct answer is option (c).