Question

The three angles of a triangle are in the ratio 1 : 2 : 1 . Find all the angles​

Answer 1

To ғɪɴᴅ :

• we need to find all angles of triangle.

Given :

• Ratio of three angles = 1 : 2 : 1

Let the three angles of triangle be 1x , 2x and 1x.

As we know that ,

• 〈 Sum of all angles of triangle = 180 〉

So,

⟶ x + 2x + x = 180

⟶ 2x + 2x = 180

⟶ 4x = 180

⟶ x = 180/4

⟶ x = 45

• All angels of triangle are :-

⇛x = 45°

⇛2x = 2 × 45 = 90°

⇛x = 45°

⚘ Verification :

〈Sum of all angles of triangle = 180〉

So,

⇛x + 2x + x = 180

⇛45 + 90 + 45 = 180

⇛90 + 90 = 180

⇛180 = 180

LHS = RHS

Hence, Verified.

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Answer 2

Given :

• Three Angles of triangle are in the ratio 1 : 2 : 1

To Find :

• All the Angles

SOLUTION :

Suppose that angles of triangle = x, 2x, x

We know that Sum of All Angles Of triangle = 180°

Therefore,

x + 2x + x = 180

4x = 180

x = 45°

Angles Of triangle :

• x = 45°
• 2x = 2×45 = 90°
• x = 45°

Verification :

x + 2x + x = 180°

Putting the value of x

45° + (2×45°) + 45° = 180°

45° + 90° + 45° = 180°

180° = 180°

Hence, VERIFIED.

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