Question

3.
If the largest angle of a triangle is twice the sum
of the other two and the smaller angle is one
fourth of the largest angle, then the angles in
degrees are
(1) 45°, 45°, 90°
(2) 30°, 60°, 90°
(3) 30°, 30°, 120°
(4) None of these​

Answer 1

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In my opinion 1st part (45°, 45°, 90°) is correct answer......

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Answer 2

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✔ANSWER:- (3)30°, 30°, 120°

⭐EXPLAINATION⭐

Let the angles of the triangle be x,y and z.

Let x be the largest angle.

Let x be the smallest angle.

According to the question,

2(y+z)=x.... (1)

Let us find the value of z,

y+z=×/2

z=(x/2)-y

z=(x-2y)/2..... (2)

According to question,

z=×/4.... (3)

Equating equation (2) and (3),

z=(x-2y)/2=×/4

(x-2y)/2=×/4

By cross multiplication,

4 (x-2y)=2x

4x-8y=2x

(-8y)=2x-4x

(-8y)=(-2x)

8y=2x

y=(2x)/8

y=x/4..... (4)

Therefore by equation (3) and (4), angle y and z are equal.

HERE OPTION (2) GETS CANCELLED.

LET'S LOOK AT OPTION (1),

The largest angle = 90°

The rest angles equal half of the largest angle that is 45°.

But the rest angles are one fourth of largest angle.

Hence,

THE OPTION (1) IS CANCELLED.

NOW, LOOKING AT OPTION (3);

The largest angle = 120°

Rest angles= 30°

We can clearly say that other angles are one fourth of the largest angle.

Hence, OPTION (3) IS CORRECT.

⭐HOPE IT HELPS UHH #CHEERS⭐