Question

The angles in a triangle are such that one angle is 30 degrees more than the smallest angle while the third angle is four times as large as the smallest angle find the measure are of all three angles

Answer 1

The sum of angles is 180.

`\alpha + \beta + \gamma = 180`

`\alpha + ( \alpha + 30) + (4 \alpha ) = 180`

`6 \alpha = 150`

`\alpha = 25 \\ \beta= 25+30=55 \\ \gamma= 4.25 =100`

Answer 2

25, 55, 100

Explanation:

Let's call the smallest angle x, therefore the other two angles would be x + 30 and 4x. Since the sum of angles in a triangle is 180° we can write:

x + x + 30 + 4x = 180

6x + 30 = 180

6x = 150

x = 25°

x + 30 = 25 + 30 = 55°

4x = 25 * 4 = 100°