The angles of a triangle measure (x+10)°

Question

, (x+20)°
, and (x+30)°
. Find the measure of the smallest angle.(1 point)
Responses

50°
50 degrees

70°
70 degrees

40°
40 degrees

60°
60 degrees
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Answer 1

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

Given the angles:

1. \( (x + 10)° \)
2. \( (x + 20)° \)
3. \( (x + 30)° \)

We can set up the equation:

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

Simplifying this equation:

\[ 3x + 60 = 180 \]

Next, we subtract 60 from both sides:

\[ 3x = 120 \]

Now, we divide by 3:

\[ x = 40 \]

Now we can find the measures of the angles by substituting \( x \) back into the expressions for the angles:

1. \( (x + 10) = 40 + 10 = 50° \)
2. \( (x + 20) = 40 + 20 = 60° \)
3. \( (x + 30) = 40 + 30 = 70° \)

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

Therefore, the measure of the smallest angle is:

50°