Question

Use the Triangle Angle Sum Theorem to find the largest angle in a triangle with angle measures of (x−20)°
, (3x+3)°
, and (2x−7)°
.(1 point)

Answer 1

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:

1. \( (x - 20)^\circ = (34 - 20)^\circ = 14^\circ \)
2. \( (3x + 3)^\circ = (3(34) + 3)^\circ = (102 + 3)^\circ = 105^\circ \)
3. \( (2x - 7)^\circ = (2(34) - 7)^\circ = (68 - 7)^\circ = 61^\circ \)

Now we list the angles:

- \( 14^\circ \)
- \( 105^\circ \)
- \( 61^\circ \)

The largest angle is:

\[
\boxed{105^\circ}
\]