Question

A triangle is sitting on a horizontal line. The bottom left interior angle of the triangle is (9 + k) degrees. The exterior angle to the bottom left interior angle is (5 k minus 3) degrees.
What is the value of k?

k = 28
k = 29
k = 31
k = 42

Answer 1

To solve for \( k \), we start by using the relationship between interior and exterior angles. The exterior angle measures \( 5k - 3 \) degrees, and we know that it is equal to \( 180^\circ - (9 + k)^\circ \) because the exterior angle and its corresponding interior angle are supplementary.

We can set up the equation as follows:

\[
5k - 3 = 180 - (9 + k)
\]

Now, simplify the equation:

\[
5k - 3 = 180 - 9 - k
\]
\[
5k - 3 = 171 - k
\]

Next, add \( k \) to both sides:

\[
5k + k - 3 = 171
\]
\[
6k - 3 = 171
\]

Then, add 3 to both sides:

\[
6k = 171 + 3
\]
\[
6k = 174
\]

Now, divide both sides by 6:

\[
k = \frac{174}{6}
\]
\[
k = 29
\]

Thus, the value of \( k \) is \( \boxed{29} \).