Question

The angles of a triangle measure 18x, x+65, and 4x. Find the value of x

Answer 1

To find the value of \( x \) in the triangle with angles measuring \( 18x \), \( x + 65 \), and \( 4x \), we can use the fact that the sum of the angles in a triangle is always \( 180^\circ \).

We can set up the equation:

\[
18x + (x + 65) + 4x = 180
\]

Now, combine the terms:

\[
18x + x + 65 + 4x = 180
\]

This simplifies to:

\[
23x + 65 = 180
\]

Next, we can isolate \( 23x \) by subtracting \( 65 \) from both sides:

\[
23x = 180 - 65
\]

Calculating the right side:

\[
23x = 115
\]

Now, we solve for \( x \) by dividing both sides by \( 23 \):

\[
x = \frac{115}{23} = 5
\]

Thus, the value of \( x \) is

\[
\boxed{5}
\]

To verify, we can substitute \( x \) back into the expressions for the angles:

1. \( 18x = 18(5) = 90^\circ \)
2. \( x + 65 = 5 + 65 = 70^\circ \)
3. \( 4x = 4(5) = 20^\circ \)

Adding these angles:

\[
90 + 70 + 20 = 180^\circ
\]

Since the sum of the angles equals \( 180^\circ \), our solution is confirmed. The value of \( x \) is indeed

\[
\boxed{5}
\]