Question

One angel of a quadrilateral is 180°.the other three Angeles are in ratio 3:4:5. Find these anggles

Answer 1

Answer:

Sum of all angles of a Quadrilateral is 360°

If one of Angle is 180° then rest of three Angles sum total of 180°

• Given Angles Ratio - 3 : 4 : 5

⇢ Sum of rest 3 Angles ≡ 180°

⇢ (3 + 4 + 5) ≡ 180°

⇢ 12 ≡ 180°

⇢ 1 ≡ 180° ÷ 12

⇢ 1 ≡ 15°

• Other Angles of Quadrilateral :

⇒ 3 : 4 : 5

• Multiplying Each by 15°

⇒ (3 × 15°) : (4 × 15°) : (5 × 15°)

⇒ 45° ; 60° ; 75°

∴ Other Angles are 45°, 60° and 75°.

Answer 2

Given

✭ One angle of a quadrilateral is 180°

✭ The other three angles are of the ratio 3:4:5

To Find

◈ The other angles?

Solution

Concept

So we shall first find what is the sum of the angles in a quadrilateral (360°). Then let's assume the ratios with x. Then equating these ratios to 360° will give us the value of x which later will give us the other angles!!

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The sum of angles of a figure is given by,

(n-2) * 180°

• N = Number of sides = 4

Substituting the values,

➝ (n-2) * 180°

➝ (4-2) * 180°

➝ 2 × 180°

➝ Angles in a quadrilateral add up to 360°

Now let the angles be,

✪ Angle¹ = 180°

✪ Angle² = 3x

✪ Angle³ = 4x

✪ Angle⁴ = 5x

Adding up these angles,

➳ 180°+3x+4x+5x = 360°

➳ 180°+12x = 360°

➳ 12x = 360°-180°

➳ 12x = 180°

➳ x = 180/12

➳ x = 15

So then the Angles will be,

»» 3x = 3(15) = 45°

»» 4x = 4(15) = 60°

»» 5x = 5(15) = 75°

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