Question

The measures of angles of a triangle are in the ratio 5:6:7 then the smallest angle of the triangle has the measure______.​

Answer 1

Step-by-step explanation:

1st angle = ${5x}$

2nd angle = ${6x}$

3rd angle = ${7x}$

Sum of all angles = 180°

${5x+6x+7x}$ ${= 180}$°

${5x+13x = 180}$°

${18x = 180}$°

${x =} \frac{180}{18}$

${x = 10}$°

1st angle = ${5x}$

= ${5}$ × ${10}$

= ${50}$°

2nd angle = ${6x}$

= ${6}$ × ${10}$

= ${60}$°

3rd angle = ${7x}$

= $7$ × $10$

= $70$°

Hence the smallest angle of the triangle is ${50}$°

Hope it helps