Question

One angle in a triangle measures twice the smallest angle, while the largest angle is six times the smallest angle. Find the measures of all three angles.

Answer 1

Answer:

Use a variable (x) for the smallest angle (call it angle 1).

 

Angle 1 = x

 

The second angle is twice the smallest angle (2x)

 

The largest angle is 6 times the smallest angle (6x)

 

Take the sum of all three of those angles and make an equation,  equal to 180.

 

x + 2x + 6x = 180

 

9x = 180  (combined like terms)

 

x = 20  (divide by 6)

 

Angle 1 (x) = 20

 

Angle 2 (2x) = 40

 

Angle 3 (6x) = 120

Answer 2

Details provided :-

One angle in a triangle measures twice the smallest angle, while the largest angle is six times the smallest angle.

Question :-

Find the measures of all three angles.

Solution :-

• Let the smallest angle be n.
• 2nd angle = twice the smallest angle = 2n
• largest angle = six times the smallest angle = 6n

(We know that all the angles of a triangle sum up to 180° in total)

According to question,

n + 2n + 6n = 180

=> 9n = 180

=> n = 180/9 = 20

Therefore,

smallest angle = n = 20°

second angle = 2n = 40°

largest angle = 6n = 120°