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

40°
40 degrees

50°
50 degrees

60°

Answer 1

To find the measure of the angles of the triangle, we use the fact that the sum of the angles in a triangle is always 180 degrees.

Given the angles:
- Angle 1: \( (x + 10)^\circ \)
- Angle 2: \( (x + 20)^\circ \)
- Angle 3: \( (x + 30)^\circ \)

We can set up the equation:

\[
(x + 10) + (x + 20) + (x + 30) = 180
\]

Combining like terms:

\[
3x + 60 = 180
\]

Now, let's solve for \( x \):

\[
3x = 180 - 60
\]
\[
3x = 120
\]
\[
x = 40
\]

Now, we can find the actual measures of the angles:

- Angle 1: \( x + 10 = 40 + 10 = 50^\circ \)
- Angle 2: \( x + 20 = 40 + 20 = 60^\circ \)
- Angle 3: \( x + 30 = 40 + 30 = 70^\circ \)

The measures of the angles are \( 50^\circ \), \( 60^\circ \), and \( 70^\circ \).

Therefore, the smallest angle is \( 50^\circ \).

The correct response is **50°**.