Question

the angles of a triangle are in the ratio 3:7:8, then find the sum of the largest and smallest angle​

Answer 1

ANSWER

The ratio of angles of triangles are 3:7:8

Let the measures of triangles are 3x,7x,8x.

⇒  3x+7x+8x=180o         [ Sum of angles of triangle is 180o ]

⇒  18x=180o

⇒  x=18180o=10o

⇒  3x=3×10o=30o

⇒  7x=7×10o=70o

⇒  8x=8×10o=80o

∴  Greatest and the smallest angles are 80o and 30o.

Answer 2

Given:

1. Angles of a Triangle are in the ratio 3:7:8

To find:

• Largest angle + Smallest Angle = ?

Method:

Let the angles be 3x, 7x and 8x

By Angle Sum Property,

3x + 7x + 8x = 180°

⇒ 18x = 180°

⇒ x = 180 ÷ 18

⇒ x = 10

Now let's Calculate sides of the Triangle

• 3x = 3(10) = 30°

• 7x = 7(10) = 70°

• 8x = 8(10) = 80°

From the above, We get to know that;

Largest Angle = 80°

Smallest Angle = 30°

Largest Angle + Smallest Angle

= 80° + 30°

= 110°