Question

The angles of a triangle measure (x+10)°, (×+20)°, and (×+30)°. Find the measure of the smallest angle.

Answer 1

[AI-generated answer — Bot GPT 3.5]

Let's start with the given information:

The angles of the triangle measure (x+10)°, (x+20)°, and (x+30)°.

To find the smallest angle, we need to find the minimum value of the sum of the three angles, since the angles of a triangle must add up to 180°.

So, the sum of the three angles is:
(x+10)° + (x+20)° + (x+30)° = 3x + 60°

Since the sum of the angles of a triangle is 180°, we can set up the equation:
3x + 60° = 180°

Subtract 60 from both sides:
3x = 180° - 60°
3x = 120°

Divide both sides by 3:
x = 40°

Now we can find the smallest angle by substituting x=40° into any of the expressions for the angles:

Smallest angle = (x+10)° = (40°+10)° = 50°

So, the measure of the smallest angle is 50°.