Question

find x, then find the measurement of both angles. 2x + 54 4x - 6 x = 30; both angles measure 118 degrees x = 30; both angles measure 114 degrees x = 20; both angles measure 112 degrees x = 20; both angles measure 110 degree

Explanation:

Step1: Set the two - angle expressions equal

Since the two angles are equal (assuming they are vertical angles or corresponding angles in a parallel - lines setup), we set up the equation $2x + 54=4x - 6$.

Step2: Solve for x

Subtract $2x$ from both sides: $54 = 4x-2x - 6$, which simplifies to $54 = 2x - 6$. Then add 6 to both sides: $54 + 6=2x$, so $60 = 2x$. Divide both sides by 2: $x=\frac{60}{2}=30$.

Step3: Find the measure of the angles

Substitute $x = 30$ into the first angle expression $2x+54$. We get $2\times30 + 54=60 + 54=114$. Substitute $x = 30$ into the second angle expression $4x - 6$, we get $4\times30-6=120 - 6 = 114$.

Answer:

$x = 30$; both angles measure 114 degrees