Question

One angle of a triangle is 30° more than the smallest angle. The largest angle is the sum of the other angles. Find the measures of all three angles.

Answer 1

Answer: $\boxed{30^{\circ}, 60^{\circ}, 90^{\circ}}$

Step-by-step explanation:

Let the smallest angle be x.

Then, the middle angle is x+30.

The largest angle is 2x+30.

Angles in a triangle add to 180 degrees, so:

$x+x+30+2x+30=180\\\\4x+60=180\\\\4x=120\\\\x=30$

So, the angles measure $\boxed{30^{\circ}, 60^{\circ}, 90^{\circ}}$