Question

The sum of the two angles in a triangle is ${95}^{\circ }$ and their difference is ${25}^{\circ }$. Then which of the following are true?

• A. 75°, 50°, 55°
• B. 85°, 65°, 30°
• C. 50°, 45°, 85°
• D. 60°, 35°, 85°

Answer 1

Answer: (A), (C), (D)

The correct options are
A

75°, 50°, 55°

C

50°, 45°, 85°

D

60°, 35°, 85°

Let the two angles be $x$ and $y$.

So, $x+y={95}^{\circ }$

$\Rightarrow x={95}^{\circ }-y$ $\cdot \cdot \cdot$ (i)

and, $x-y={25}^{\circ }$ $\cdot \cdot \cdot$ (ii)

Substitute (i) in (ii),

$\Rightarrow {95}^{\circ }-y-y={25}^{\circ }$

$\Rightarrow {95}^{\circ }-2y={25}^{\circ }$

$\Rightarrow y=\frac{{95}^{\circ }-{25}^{\circ }}{2}$

$\Rightarrow y={35}^{\circ }$

So, $x={95}^{\circ }-{35}^{\circ }$

$\Rightarrow$ $x={60}^{\circ }$

Third angle is ${180}^{\circ }-{95}^{\circ }={85}^{\circ }$

So, the angles are ${35}^{\circ }$, ${60}^{\circ }$ and ${85}^{\circ }$.