Questions: Find the value of x.

Transcript text: Find the value of $x$.

Solution

Step 1: Identify the given angles and their relationships

The problem provides two angles: $5x - 10^\circ$ and $60^\circ$. These angles are vertical angles, which means they are equal.

Step 2: Set up the equation

Since vertical angles are equal, we can set up the equation: \[ 5x - 10 = 60 \]

Step 3: Solve for $x$

Add 10 to both sides of the equation to isolate the term with $x$: \[ 5x - 10 + 10 = 60 + 10 \] \[ 5x = 70 \]

Divide both sides by 5 to solve for $x$: \[ x = \frac{70}{5} \] \[ x = 14 \]

The value of $x$ is $14$.

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