Question

The second angle of an architect’s triangle is three times as large as the first. The third angle is 30 more than the first. Find the measure of each angle.

Answer 1

30°, 60° and 90°

Explanation:

The sum of the 3 angles in a triangle = 180°

let x be the first angle, then the second angle is 3x and the third angle is x + 30

Sum the 3 angles and equate to 180

x + 3x + x + 30 = 180

5x + 30 = 180 ( subtract 30 from both sides )

5x = 150 ( divide both sides by 5 )

x = 30

first angle = x = 30°

second angle = 3x = 3 × 30° = 90°

third angle = x + 30 = 30 + 30 = 60°