Question

try it! 2. find the value of x and the measure of each labeled angle. a. (6x - 45)° (4x + 5)° notebook enter note here

Explanation:

Step1: Set the angles equal

Since vertical angles are equal, we set $6x - 45=4x + 5$.

Step2: Solve for x

Subtract $4x$ from both sides: $6x-4x - 45=4x-4x + 5$, which simplifies to $2x-45 = 5$. Then add 45 to both sides: $2x-45 + 45=5 + 45$, getting $2x=50$. Divide both sides by 2: $x=\frac{50}{2}=25$.

Step3: Find the measure of the angles

Substitute $x = 25$ into $6x - 45$: $6\times25-45=150 - 45=105$. Substitute $x = 25$ into $4x + 5$: $4\times25+5=100 + 5=105$.

Answer:

$x = 25$, and the measure of each labeled angle is $105^{\circ}$