Question

what are the measures of the marked angles? (3x - 8)° (2x + 1)° 19° 27° 38° 90°

Explanation:

Step1: Set up equation

The two marked angles are vertical angles, and vertical angles are equal. So we set up the equation $3x - 8=2x + 1$.

Step2: Solve for x

Subtract $2x$ from both sides: $3x-2x - 8=2x-2x + 1$, which simplifies to $x-8 = 1$. Then add 8 to both sides: $x=1 + 8$, so $x = 9$.

Step3: Find the measure of the angle

Substitute $x = 9$ into the expression for one of the angles, say $2x+1$. Then $2\times9+1=18 + 1=19$.

Answer:

$19^{\circ}$