Question

The diagram shows a triangle.
35°
67°
6w
What is the value of w?
w =
°

Answer 1

To find the value of \( w \) in the given triangle, we can use the fact that the sum of the interior angles of a triangle is always \( 180^\circ \).

Let's denote the angles of the triangle as follows:
- Angle 1: \( 35^\circ \)
- Angle 2: \( 67^\circ \)
- Angle 3: \( 6w \)

According to the angle sum property:

\[
35^\circ + 67^\circ + 6w = 180^\circ
\]

First, we want to sum up the known angles:

\[
35^\circ + 67^\circ = 102^\circ
\]

Now we can substitute this back into the equation:

\[
102^\circ + 6w = 180^\circ
\]

Next, we will isolate \( 6w \) by subtracting \( 102^\circ \) from both sides:

\[
6w = 180^\circ - 102^\circ
\]
\[
6w = 78^\circ
\]

Now, we can solve for \( w \) by dividing both sides by 6:

\[
w = \frac{78^\circ}{6} = 13^\circ
\]

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

\[
\boxed{13}
\]