Question

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

50°
50 degrees

60°
60 degrees

40°
40 degrees

70°

Answer 1

To find the measure of the smallest angle in the triangle, we start by using the fact that the sum of the angles in a triangle is always 180 degrees.

The angles of the triangle are given as:
- 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 the terms gives:
\[
3x + 60 = 180
\]

Next, we solve for \( x \):
\[
3x = 180 - 60
\]
\[
3x = 120
\]
\[
x = 40
\]

Now, we can find the measures of the angles:
1. \( (x + 10) = (40 + 10) = 50^\circ \)
2. \( (x + 20) = (40 + 20) = 60^\circ \)
3. \( (x + 30) = (40 + 30) = 70^\circ \)

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

Thus, the smallest angle is:
**50°**