Questions: What is the measure of the angles? 13° 145° 35° 180°

Transcript text: What is the measure of the angles? $13^{\circ}$ $145^{\circ}$ $35^{\circ}$ $180^{\circ}$

Solution

Step 1: Set up the equation

Since the angles are vertical angles, they are equal. Therefore, we can set the expressions for the angles equal to each other: \[ 3x - 4 = 2x + 9 \]

Step 2: Solve for $ x $

Subtract $ 2x $ from both sides to isolate $ x $ on one side: \[ 3x - 2x - 4 = 2x - 2x + 9 \] \[ x - 4 = 9 \]

Add 4 to both sides to solve for $ x $: \[ x - 4 + 4 = 9 + 4 \] \[ x = 13 \]

Step 3: Substitute $ x $ back into the expression to find the angle

Substitute $ x = 13 $ back into either expression for the angle. Using $ 3x - 4 $: \[ 3(13) - 4 = 39 - 4 = 35 \]

The measure of the angles is $ 35^\circ $.

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