To find the largest angle in the triangle with angle measures of \( (x - 20)^\circ \), \( (3x + 3)^\circ \), and \( (2x - 7)^\circ \), we'll first apply the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is 180 degrees.
So we set up the equation:
\[ (x - 20) + (3x + 3) + (2x - 7) = 180 \]
Now, let's combine like terms:
\[ x - 20 + 3x + 3 + 2x - 7 = 180 \] \[ (1x + 3x + 2x) + (-20 + 3 - 7) = 180 \] \[ 6x - 24 = 180 \]
Next, we solve for \( x \):
\[ 6x = 180 + 24 \] \[ 6x = 204 \] \[ x = \frac{204}{6} = 34 \]
Now that we have the value of \( x \), we can find each angle:
- \( (x - 20)^\circ = (34 - 20)^\circ = 14^\circ \)
- \( (3x + 3)^\circ = (3(34) + 3)^\circ = (102 + 3)^\circ = 105^\circ \)
- \( (2x - 7)^\circ = (2(34) - 7)^\circ = (68 - 7)^\circ = 61^\circ \)
Now we list the angles:
- \( 14^\circ \)
- \( 105^\circ \)
- \( 61^\circ \)
The largest angle is:
\[ \boxed{105^\circ} \]
1 answer