Question

Use the Triangle Sum Theorem to find the largest angle in a triangle with angle measures (2x-20)°, (2x+34)°, and (x+11)°.
*
1 point

Answer 1

The Triangle Sum Theorem states that the sum of the angles in a triangle is 180°.

We need to set up an equation using the given angles:

\[
(2x - 20) + (2x + 34) + (x + 11) = 180
\]

Now, combine the like terms:

\[
2x - 20 + 2x + 34 + x + 11 = 180
\]
\[
(2x + 2x + x) + (-20 + 34 + 11) = 180
\]
\[
5x + 25 = 180
\]

Next, solve for \(x\):

\[
5x = 180 - 25
\]
\[
5x = 155
\]
\[
x = 31
\]

Now, substitute \(x = 31\) back into the expressions for the angles to find their measures:

1. First angle:
\[
2x - 20 = 2(31) - 20 = 62 - 20 = 42°
\]

2. Second angle:
\[
2x + 34 = 2(31) + 34 = 62 + 34 = 96°
\]

3. Third angle:
\[
x + 11 = 31 + 11 = 42°
\]

Now we have the three angles of the triangle:
- \(42°\)
- \(96°\)
- \(42°\)

The largest angle is:

\[
\boxed{96°}
\]