Question

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

70°
70
°
70 degrees

60°
60
°
60 degrees

40°
40
°
40 degrees

50°

Answer 1

To find the angles of the triangle, we start by setting up the equation for the sum of the angles in a triangle, which is 180°.

The angles are given as:
- First angle: \( (x + 10)° \)
- Second angle: \( (x + 20)° \)
- Third angle: \( (x + 30)° \)

We can set up the equation:

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

Simplifying the left side:

\[
3x + 60 = 180
\]

Now, we isolate \( x \):

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

Now, we can find each angle by substituting \( x = 40 \) back into the expressions for the angles:

1. First angle:
\[
(x + 10) = (40 + 10) = 50°
\]

2. Second angle:
\[
(x + 20) = (40 + 20) = 60°
\]

3. Third angle:
\[
(x + 30) = (40 + 30) = 70°
\]

Now we have the measures of the angles: 50°, 60°, and 70°.

The smallest angle is \( 50° \).

So, the answer is \( 50° \).