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