Question

Use the Triangle Angle Sum Theorem to find the measure of the largest angle of a triangle with angle measures 3x+10,2x-3 and 5x
A 61.9
B 31.6
C 86.5
D 83.5

Answer 1

The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is 180 degrees. Given the angle measures \(3x + 10\), \(2x - 3\), and \(5x\), we can use this property to find the values of \(x\) and the measures of the angles.

Set up the equation based on the Triangle Angle Sum Theorem:

\[
(3x + 10) + (2x - 3) + (5x) = 180
\]

Now, combine like terms:

\[
3x + 10 + 2x - 3 + 5x = 180
\]

This simplifies to:

\[
(3x + 2x + 5x) + (10 - 3) = 180
\]
\[
10x + 7 = 180
\]

Next, subtract 7 from both sides:

\[
10x = 180 - 7
\]
\[
10x = 173
\]

Now, divide by 10:

\[
x = 17.3
\]

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

1. For the angle \(3x + 10\):

\[
3(17.3) + 10 = 51.9 + 10 = 61.9
\]

2. For the angle \(2x - 3\):

\[
2(17.3) - 3 = 34.6 - 3 = 31.6
\]

3. For the angle \(5x\):

\[
5(17.3) = 86.5
\]

Now that we have the angles:

- \(3x + 10 = 61.9^\circ\)
- \(2x - 3 = 31.6^\circ\)
- \(5x = 86.5^\circ\)

The largest angle is:

\[
\boxed{86.5^\circ}
\]

So, the measure of the largest angle of the triangle is \(86.5^\circ\) (Option C).