To find the measure of the smallest angle in the triangle, we first need to set up an equation using the fact that the sum of the angles in any triangle is always 180 degrees.
Given the angles:
- \( (x + 10)^\circ \)
- \( (x + 20)^\circ \)
- \( (x + 30)^\circ \)
We can set up the following equation:
\[ (x + 10) + (x + 20) + (x + 30) = 180 \]
Simplifying the left side:
\[ 3x + 60 = 180 \]
Now, we solve for \( x \):
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Subtract 60 from both sides: \[ 3x = 120 \]
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Divide by 3: \[ x = 40 \]
Now that we have the value of \( x \), we can find the measures of the angles:
- \( (x + 10) = (40 + 10) = 50^\circ \)
- \( (x + 20) = (40 + 20) = 60^\circ \)
- \( (x + 30) = (40 + 30) = 70^\circ \)
The three angles are:
- 50°
- 60°
- 70°
The smallest angle is \( 50^\circ \).
Therefore, the measure of the smallest angle is 50 degrees.