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Answer 1

Correct Question :- If the angles of a triangle are in the ratio 1:2:3, then the smallest angle of a triangle?

Given :- The angles of a triangle are in the ratio 1:2:3.

To find :- The smallest angle of a triangle?

Solution :-

Let us assume that, the three angles of a triangle is 1x, 2x and 3x respectively.

we know that,

• The sum of all three angles of a triangle is 180°.

This statement is also known as angle sum property of a triangle.

⠀

so,

→ All three given angles sum = 180° {By angle sum property of a quadrilateral.}

putting all values,

→ 1x + 2x + 3x = 180

→ 3x + 3x = 180

→ 6x = 180

→ x = 180/6

→ x = 30.

Therefore,

• 1x = 1 * 30 = 30°.
• 2x = 2 * 30 = 60°.
• 3x = 3 * 30 = 90°.

Now, here by seeing all the angles of a triangle we can say that 60° is the smallest angle in a triangle.

⠀

Hence the smallest angle of a triangle is 60°.

Answer 2

Answer:

Correct Question :-

• If the angles of a triangle are in the ratio of 1 : 2 : 3, then the smallest angle of the triangle is ?

Given :-

• The angles of a triangle are in the ratio of 1 : 2 : 3.

To Find :-

• What is the smallest angle of the triangle.

Solution :-

Let,

◆ First angle be x

◆ Second angle be 2x

◆ Third angle will be 3x

As we know that :

★ Sum of all angles of a triangle = 180° ★

According to the question by using the formula we get,

↦ x + 2x + 3x = 180°

↦ 3x + 3x = 180°

↦ 6x = 180°

↦ x = 180°/6

➠ x = 30°

Hence, the required angles of a triangle are :

➲ First angle :

↦ x

➠ 30°

➲ Second angle :

↦ 2x

↦ 2(30°)

↦ 2 × 30°

➠ 60°

And,

➲ Third angle :

↦ 3x

↦ 3(30°)

↦ 3 × 30°

➠ 90°

∴ The smallest angle of a triangle is 30° .

VERIFICATION :

↦ x + 2x + 3x = 180°

Now, by putting x = 30° we get,

↦ 30° + 2(30°) + 3(30°) = 180°

↦ 30° + 60° + 90° = 180°

↦ 90° + 90° = 180°

➠ 180° = 180°

Hence, Verified .