Question

One angle of a triangle is ${61}^{\circ }$ and the other two angles are in the ratio $\left(\frac{3}{2}\right):\left(\frac{4}{3}\right)$. Find the smallest angle in the triangle.

• A. ${56}^{\circ }$
• B. ${59}^{\circ }$
• C. ${61}^{\circ }$
• D. ${63}^{\circ }$

Answer 1

The correct option is A

${56}^{\circ }$

Let the other angles be $\left(\frac{3}{2}\right)x^{\circ }$ and $\left(\frac{4}{3}\right)x^{\circ }$

Then, according to the angle sum property, ${61}^{\circ }+\left(\frac{3}{2}\right)x+\left(\frac{4}{3}\right)x={180}^{\circ }$

$\frac{(9x+8x)}{6}={180}^{\circ }-{61}^{\circ }={119}^{\circ }$

$17x={119}^{\circ }\times 6$

$x=\frac{({119}^{\circ }\times 6)}{17}={42}^{\circ }$

$\left(\frac{3}{2}\right)x={63}^{\circ }$

$\left(\frac{4}{3}\right)x={56}^{\circ }$

Hence, the smallest angle is ${56}^{\circ }$.