Question

The angles of a cyclic quadrilateral are in the ratio 1:2:3:4. What is the measure of the smallest angle?

• A. 36°
• B. 72°
• C. 108°
• D. 144°

Answer 1

Answer:

A. 36°

In a cyclic quadrilateral, opposite angles sum to (180^\circ).

Let the angles be:
$x,\ 2x,\ 3x,\ 4x$

Sum of angles in any quadrilateral:
$x + 2x + 3x + 4x = 10x = 360^\circ$

$10x=360^\circ \Rightarrow x=36^\circ$

So the angles are:

• $(36^\circ, 72^\circ, 108^\circ, 144^\circ)$

Smallest angle = 36°.