Question

The angles of a triangle ABC are in the ratio 1 : 2 : 3, show this information in pie diagram.

Answer 1

1. Find the angles of the triangle

By the angle sum property, the interior angles of a triangle always add up to 180°. Given the ratio 1 : 2 : 3, let the angles be x, 2x and 3x.

x + 2x + 3x = 180°

6x = 180°

⇒ x = 30°

Thus, the measures of the triangle’s angles are:

∠A = 1 × 30° = 30°

∠B = 2 × 30° = 60°

∠C = 3 × 30° = 90°

2. Calculate the central angles for the pie diagram

A pie diagram represents data out of a total central angle of 360°. We find each sector’s angle using its proportion:

Central angle = `"Component value"/"Total value" xx 360^circ`

Section A (∠A = 30°):

`(30^circ)/(180^circ) xx 360^circ` = 60°

Section B (∠B = 60°):

`(60^circ)/(180^circ) xx 360^circ` = 120°

Section C (∠C = 90°):

`(90^circ)/(180^circ) xx 360^circ` = 180°

3. Visual representation (Pie diagram)

The angles of triangle ABC are 30°, 60° and 90°, which map onto a pie diagram with sector central angles of 60°, 120° and 180° respectively.