Question

Q.12. If the angles of triangle are in the ratio 2:3: 4 find the three angles
(a) 20°, 90°, 70°
(b) 40°, 60°, 80°
(c) 45°, 45°, 90°
(d) none of these.​

Answer 1

Given:-

• The angles of triangle are in the ratio 2:3:4.

To Find:-

• The value of three angles.

Concept used:-

• Angle sum Property :- Sum of three angles of a triangle is 180°.

Now,

Let the Ratio of angles be "x"

• First angle = 2x

• Second angle = 3x

• Third angle = 4x.

Again,

→ 2x + 3x + 4x = 180°

→ 9x = 180

→ x = 180/9

→ x = 20.

So, The Value of x is 20°.

Therefore,

→ First angle = 2x → 40°

→ Second angle = 3x → 60°

→ Third angle = 4x → 80°

Hence, The value of angles of triangle is 40° , 60° and 80°.

Answer 2

Given:

• Three angles of a triangle are in ratio 2:3:4

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Need to find:

• The three angles =?

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Solution:

• we know sum of all angles of a triangle = 180°
• let the three angles be 2x, 3x and 4x

Now,

2x + 3x+ 4x= 180°

⟹9x = 180°

⟹x= 180° ÷ 9

$\purple{\implies x= 20 \degree}$

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Now the angles are:

2x:

=2× 20°

= $\red{\bold{40 \degree}}$

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3x:

=3× 20°

= $\red{\bold{60 \degree}}$

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4x:

=4× 20°

= $\red{\bold{80 \degree}}$

• Three angles if the triangle measure 40°, 60° and 80°