Question

the second angle of a triangle is double the first. the third angle is 40 less than the first. find the three angles​

Answer 1

Step-by-step explanation:

A = 27

O = 81

B = 72

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Answer 2

Given :–

• The second angle of a triangle is double the first angle.
• The third angle of a triangle is 40 less than the first angle.

To Find :–

• All the three angles.

Solution :–

Let,

• The first angle be x.

The second angle is double than the first angle.

So, first angle × 2.

It means,

• Second angle = 2x

The third angle is 40 less than the first angle.

So, Forst angle – 40.

It means,

• Third angle = x – 40

We know that,

Sum of all the angles of a triangle = 180°

⟹ first angle + second angle + third angle = 180°

⟹ x + 2x + x – 40 = 180°

⟹ 4x – 40 = 180°

⟹ 4x = 180° + 40

⟹ 4x = 220°

⟹ x = $\sf \dfrac{220}{4}$

Cut the denominator and the numerator by 2, we obtain

⟹ x = $\sf \dfrac{110}{2}$

Again, cut the denominator and the numerator by 2, we obtain

⟹ x = 55°

• x = 55°

So the angles will be :–

• 1st angle = x = 55°
• 2nd angle = 2x = 2 × 55° = 110°
• 3rd angle = x – 40 = 55° – 40 = 15°

Check :–

We know that,

Sum of all angles of a triangle = 180°

⟹ 1st angle + 2nd angle + 3rd angle = 180°

⟹ 55° + 110° + 15° = 180°

⟹ 70° + 110° = 180°

⟹ 180° = 180°

L.H.S. = R.H.S.

Hence, the L.H.S. is equal to the R.H.S.

So, the answer is correct.