Question

A triangle with exterior angles is shown. The bottom right angle of the triangle is (3 h + 18) degrees. The bottom right exterior angle is (15 h) degrees.
What is the value of h?

h = 1.5
h = 9
h = 10
h = 13.5

Answer 1

To solve for \( h \) in the given triangle with its angles, we first recall the relationship between an exterior angle and the interior angles of a triangle. The exterior angle is equal to the sum of the two remote interior angles.

In this case, we have the bottom right interior angle represented as \( 3h + 18 \) degrees, and the corresponding exterior angle is represented as \( 15h \) degrees.

By the property of exterior angles, we know that:

\[
\text{Exterior angle} = \text{Interior angle} + \text{Another interior angle}
\]

For our case, we specifically want to state that the exterior angle is equal to the corresponding interior angle, since the relevant two angles are adjacent to the exterior angle being considered.

Thus, we can write the equation as:

\[
15h = 3h + 18
\]

Now, we'll solve this equation for \( h \):

1. Subtract \( 3h \) from both sides:

\[
15h - 3h = 18
\]

2. This simplifies to:

\[
12h = 18
\]

3. Now, divide both sides by 12:

\[
h = \frac{18}{12}
\]

4. Simplifying the fraction gives:

\[
h = \frac{3}{2} = 1.5
\]

Thus, the value of \( h \) is:

\[
\boxed{1.5}
\]