Question

In a quadrilateral the ratio of angles is 1 : 2 : 3 : 4. ∴ The largest angle is ______.

Options

• 120°

• 150°

• 140°

• 144°

Answer 1

In a quadrilateral the ratio of angles is 1 : 2 : 3 : 4. ∴ The largest angle is 144°.

Explanation:

Step 1: Set up the equation

The sum of the interior angles of any quadrilateral is 360°. Given the ratio of the angles is 1 : 2 : 3 : 4, let the angles be represented as  x, 2x, 3x and 4x. The sum of these angles must equal 360°.

x + 2x + 3x + 4x = 360°

Step 2: Solve for x

Combine the terms on the left side of the equation.

10x = 360°

Divide both sides by 10 to find the value of x.

`x = 360^circ/10 = 36^circ`

Step 3: Find the largest angle

The largest angle is represented by the largest ratio part, which is 4x. Substitute the value of x found in the previous step.

Largest angle = 4x = 4(36°) = 144°