Question

A triangle has angle measures of 75°
75
°
, 41°
41
°
, and (3x+19)°
(
3
𝑥
+
19
)
°
. Solve for x.(1 point)

Answer 1

In a triangle, the sum of the angles is always \(180^\circ\). Given the angles:

1. \(75^\circ\)
2. \(41^\circ\)
3. \( (3x + 19)^\circ \)

We can set up the equation:

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

Now, let's simplify the left side:

\[
75 + 41 = 116
\]

So, we can rewrite the equation as:

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

Combine the constants:

\[
116 + 19 = 135
\]

Now the equation is:

\[
135 + 3x = 180
\]

Next, subtract \(135\) from both sides:

\[
3x = 180 - 135
\]
\[
3x = 45
\]

Now, divide by \(3\):

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

So, the value of \(x\) is:

\[
\boxed{15}
\]