Question

Question
The angles of a triangle measure (x+10)°
, (x+20)°
, and (x+30)°
. Find the measure of the smallest angle.(1 point)
Responses

70°
70 degrees

50°
50 degrees

60°
60 degrees

40°

Answer 1

To find the measure of the smallest angle in the triangle with angles measuring (x + 10)°, (x + 20)°, and (x + 30)°, we first need to find the value of \( x \) using the fact that the sum of the angles in a triangle is 180°.

1. Set up the equation:
\[
(x + 10) + (x + 20) + (x + 30) = 180
\]

2. Simplify the left side:
\[
3x + 60 = 180
\]

3. Subtract 60 from both sides:
\[
3x = 120
\]

4. Divide by 3:
\[
x = 40
\]

Now that we have \( x \), we can find the measures of the angles:

- First angle:
\[
x + 10 = 40 + 10 = 50°
\]

- Second angle:
\[
x + 20 = 40 + 20 = 60°
\]

- Third angle:
\[
x + 30 = 40 + 30 = 70°
\]

The angles of the triangle are 50°, 60°, and 70°.

The smallest angle is:
\[
\boxed{50°}
\]