Question

The angles of a quadrilayeral are in the ratio 1:2:3:4. Hence the measurement of smallest angle is

Answer 1

☆ Solution ☆

Given :-

• The angles of a quadrilayeral are in the ratio 1:2:3:4.

To Find :-

• The measurement of smallest angle

Step-by-Step-Explaination :-

As we know that :-

The sum of all angles of a quadrilateral is 360°.

Therefore,

Let the angles be x, 2x, 3x, 4x.

According to the question

=> x + 2x + 3x + 4x = 360

=> 10x = 360

=> x = $\frac{360}{10}$

=> x = 36

So,

The angles are:-

1. x = 36°

2. 2x = 2 × 36 = 72°

3. 3x = 3 × 36 = 108°

4. 4x = 4 × 36 = 144°

Answer 2

Answer:

36°

Step-by-step explanation:

Ratio = 1:2:3:4

Thus, assume angles to be x, 2x, 3x and 4x.

By Angle Sum Property of a quadrilateral(Sum of all angles in quadrilateral is 360°) :-

x + 2x + 3x + 4x = 360°

=> 10x = 360°

∴ x = 360/10 => 36°

As x is the smallest angle between x, 2x, 3x and 4x, the measure of smallest angle is 36°.