Question

One angle of a triangle is ${82}^{\circ }$ and the other two are in the ratio 3 : 4. Find the value of other two angles.

• A. ${38}^{\circ }$ and ${60}^{\circ }$
• B. ${54}^{\circ }$ and ${44}^{\circ }$
• C. ${42}^{\circ }$ and ${56}^{\circ }$
• D. ${48}^{\circ }$ and ${50}^{\circ }$
  

Answer 1

The correct option is C ${42}^{\circ }$ and ${56}^{\circ }$

Let the two angles be $3x^{\circ }$ and $4x\circ$
Using Angle Sum Property,
${82}^{\circ }+3x^{\circ }+4x^{\circ }={180}^{\circ }$
$7x={180}^{\circ }-{82}^{\circ }$
$7x={98}^{\circ }$
$x={14}^{\circ }$
Hence the other two angles are-
$3\times x=3\times 14={42}^{\circ }$
and $4\times x=4\times 14={56}^{\circ }$