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

60°
60 degrees

50°
50 degrees

40°
40 degrees
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Answer 1

To find the measure of the smallest angle in the triangle with angles measuring (x+10)°, (x+20)°, and (x+30)°, we need to use 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:

\[
x = 40
\]

5. Now, substitute \(x = 40\) back into the expressions for the angles:

- First angle: \(x + 10 = 40 + 10 = 50°\)
- Second angle: \(x + 20 = 40 + 20 = 60°\)
- Third angle: \(x + 30 = 40 + 30 = 70°\)

The smallest angle is \(50°\).

So the measure of the smallest angle is **50 degrees**.