Question

the largest angle of a triangle is twice the sum of the other two. the smallest is one-fourth of the largest. determine all the angles in degress.​

Answer 1

GIVEN :

Let the two angles be x° and y°

The largest angle of a triangle is twice the sum of the other two.

Smallest angle is one - fourth of larger angle

Largest angle = 2(x + y)

We know that,

Sum of all angles in a ∆ = 180°

According to the problem,

2(x + y) + x + y = 180°

2x + 2y + x + y = 180°

3x + 3y = 180°

3(x + y) = 180°

x + y = 180/3

x + y = 60°

Thus, largest angle = 2(x + y) = 2(60) = 120°

Smaller angle = y = 1/4 × 120 = 30°

Third angle :

x + 120° + 30° = 180°

x + 150° = 180°

x = 180° - 150°

x = 30°

Therefore, the three angles are 120°, 30° and 30°.

Answer 2

Answer:

The three angels are 30°, 30°, 120°

Step-by-step explanation:

Given Problem:

The largest angle of a triangle is twice the sum of the other two. the smallest is one-fourth of the largest. determine all the angles in degrees.​

Solution:

To Find:

The Angles.

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Method:

Let the other two angles be:

x° and y°

The largest angel = 2(x + y)

We know that,

★The sum of the angles  of a triangle = 180°★

∴ (x + y) + x + y = 180°  

⇒2x + 2y + x +y = 180

⇒ 3x + 3y = 180  

⇒x + y = 60

Given that,

The smallest angel = 1/4 (largest angel)

∴ y = 1 /4 × 120° =30°

Now,

Putting y = 30 in (2), x + 30.

Hence,

The angels are 30°, 30°, 120°

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