Question

angles of a quadrilateral are in the ratio 2:3:4:5. find these angles.

Answer 1

Question:-

angles of a quadrilateral are in the ratio 2:3:4:5. find these angles.

Answer:-

• The angles are 51.42°,77.14°,102.85° and 128.57°

To find:-

• Angles of quadrilateral

Solution:-

• Ratio = 2:3:4:5

Put x in the ratio:-

• 2x
• 3x
• 4x
• 5x

As we know,

• Sum of all angles = 360°

According to question,

$\large{ \tt : \: \implies \: \: \: \: \: \: 2x + 3x + 4x + 5x = 360 \degree}$

$\large{ \tt : \: \implies \: \: \: \: \: \: 14x = 360 \degree}$

$\large{ \tt : \: \implies \: \: \: \: \: \: x = \frac{360}{14} }$

$\large{ \tt : \: \implies \: \: \: \: \: \: x = 25.71 \degree}$

• The value of x is 25.71°

______________________

• 2x = 2×25.71 = 51.42°
• 3x = 3×25.71 = 77.14°
• 4x = 4×25.71 = 102.85°
• 5x = 5×25.71 = 128.57°

______________________

Hence,

The angles are 51.42°,77.14°,102.85° and 128.57°