Question

A triangle has angle measures of 75° , 41° , and (3x+19)° . Solve for x.

Answer 1

To find the value of \( x \), we first use the fact that the sum of the angles in a triangle is \( 180^\circ \).

We are given the angles:
- \( 75^\circ \)
- \( 41^\circ \)
- \( (3x + 19)^\circ \)

We can set up the equation:

\[
75 + 41 + (3x + 19) = 180
\]

Now, we first simplify the left side:

\[
75 + 41 = 116
\]

So the equation becomes:

\[
116 + (3x + 19) = 180
\]

Next, we simplify further by combining \( 116 \) and \( 19 \):

\[
116 + 19 = 135
\]

Now, the equation is:

\[
135 + 3x = 180
\]

To isolate \( 3x \), we subtract \( 135 \) from both sides:

\[
3x = 180 - 135
\]

Calculating the subtraction:

\[
3x = 45
\]

Now, we divide both sides by \( 3 \) to find \( x \):

\[
x = \frac{45}{3} = 15
\]

Thus, the solution is:

\[
\boxed{15}
\]