Question

The angles of a triangle are in the ratio $3:7:8$. Find the greatest and the smallest angles. The sum of the angles of a triangle is ${180}^{\circ }$.

Answer 1

Given that, angles are divided in the ratio
$3:7:8$ and their sum is ${180}^{\circ }$
i.e., ${180}^{\circ }$ is divided into $3+7+8=18$ equal parts,
Then, 3 out of 18 equal parts
$=\frac{3}{18}$ of total sum
$=\frac{3}{18}\times {180}^{\circ }$
$=3\times {10}^{\circ }={30}^{\circ }$
7 out of 18 equal parts $=\frac{7}{18}$

$=\frac{7}{18}\times {180}^{\circ }$
$=7\times 10={70}^{\circ }$
And, 8 out of 18 equal parts $=\frac{8}{18}$ of total sum
$=\frac{8}{18}\times {180}^{\circ }$
$=8\times {10}^{\circ }={80}^{\circ }$
Therefore, the largest and the smallest angle are ${80}^{\circ }\text{and}{30}^{\circ }$ among three angles respectively.