Find the size of x in the diagram.

Step 1: Identify the relationship between the angles. The image shows two angles, $2x$ and $4x$, that lie on a straight line. Angles on a straight line are supplementary, meaning their sum is $180^\circ$.

Step 2: Formulate the equation. Add the two angles and set their sum equal to $180^\circ$: $2x + 4x = 180^\circ$

Step 3: Solve for $x$. Combine the like terms on the left side of the equation: $(2 + 4)x = 180^\circ$ $6x = 180^\circ$ Divide both sides by 6 to find the value of $x$: $x = \frac{180^\circ}{6}$ $x = 30^\circ$

Step 4: Calculate the measure of each angle. Substitute the value of $x$ back into each expression: • First angle: $2x = 2 \times 30^\circ = 60^\circ$ • Second angle: $4x = 4 \times 30^\circ = 120^\circ$

The size of $x$ is $\boxed{30^\circ}$.