Question

In a quadrilateral, angles A, B, C are in the ratio 4:2:5 and fourth angle is 140 degree, then the measure of smallest angle is​

Answer 1

Given :-

• Angles given in the ratio = 4 : 2 : 5
• Fourth angle = 140°

To find :-

• Measure of the smallest angle = ?

Solution :-

Let the angles given in the ratio be :-

• 4x
• 2x
• 5x

• Sum of the angles of quadrilateral = 360°

$\mapsto$ 4x + 2x + 5x + 140° = 360°

$\mapsto$ 11x + 140° = 360°

$\mapsto$ 11x = 360° - 140°

$\mapsto$ 11x = 220°

$\mapsto$ $\sf{x~=~\dfrac{220 \degree}{11}}$

$\mapsto$ $\sf{x~=~20 \degree}$

• The value of x = 20°

$\mapsto$ Measure of all the angles :-

• 4x = 4 × 20° = 80°
• 2x = 2 × 20° = 40°
• 5x = 5 × 20° = 100°
• Fourth angle = 140° (given)

The smallest angle $\mapsto$ 40°