To find the value of angle 6, we need to set up an equation based on the relationship between angles 3 and 6 in the diagram.
Angle 3 and angle 6 are corresponding angles, which means they are equal to each other. So, we can set up the equation:
\[ \text{Angle 3} = \text{Angle 6} \]
Given:
- Angle 3 = \( 18x - 8 \)
- Angle 6 = \( 70 - 4x \)
So, we have:
\[ 18x - 8 = 70 - 4x \]
Now, let's solve for \( x \):
\[ 18x + 4x = 70 + 8 \]
\[ 22x = 78 \]
Divide both sides by 22:
\[ x = \frac{78}{22} \]
\[ x = 3.54 \]
Now that we have found the value of \( x \), we can substitute it back into the expression for angle 6 to find its value:
\[ \text{Angle 6} = 70 - 4x \]
\[ \text{Angle 6} = 70 - 4(3.54) \]
\[ \text{Angle 6} = 70 - 14.16 \]
\[ \text{Angle 6} ≈ 55.84 \]
So, angle 6 is approximately \( 55.84^\circ \).
