Question

The angles of quadrilateral are in the ratio 2:3::3:4.then the last angle in degrees is

Answer 1

Appropriate Question :-

The angles of quadrilateral are in the ratio 2:3::3:4.then the least of angle in degrees is

Solution :-

Given :

• Ratio = 2 : 3 : 3 : 4

Need to find :

• Least of angle in the quadrilateral

We know,

• Sum of angles of quadrilateral is 360°.

Let,

The angles of quadrilateral is

• 2x
• 3x
• 3x
• 4x

Now,

$\sf:\longmapsto{2x + 3x + 3x + 4x = 360 \degree} \\ \\ \sf:\longmapsto{12x = 360 \degree} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf:\longmapsto{x = \frac{360}{12} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bf:\longmapsto \red{x = 30 \degree} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

The Quadrilateral angle are :

→ 2(30)

→ 60°

→ 3(30)

→ 90°

→ 3(30)

→ 90°

→ 4(30)

→ 120°

The least of angles of quadrilateral are :

• 60°
• 90°
• 90°
• 120°

Verification :-

$\sf:\longmapsto{2x + 3x + 3x + 4x = 360} \: \: \: \: \\ \\ \sf:\longmapsto{60 + 90 + 9 0 + 120 = 360} \\ \\ \bf:\longmapsto \red{360 = 360} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

${\boxed{\bf{\green{Hence \: Verified \: ✔}}}}$

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1. the angle of quadrilateral are in the ratio 1:2:3:4 If the sum of the angels of a quadrilateral 360 degrees, find the measures of each angles.

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