Question

remember to show your thinking with your work. minimum setup of problem, value of the variable and measure of each angle. use the figure below to answer the questions. drawing not to scale m∠2 = 2x + 39 and m∠4 = x + 61 find the of angle m∠2 (substitute the x) measure of angle ∠2

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle2$ and $\angle4$ are vertical angles, so $m\angle2 = m\angle4$. Then we set up the equation $2x + 39=x + 61$.

Step2: Solve the equation for x

Subtract $x$ from both sides of the equation: $2x - x+39=x - x + 61$, which simplifies to $x+39 = 61$. Then subtract 39 from both sides: $x=61 - 39$, so $x = 22$.

Step3: Find the measure of $\angle2$

Substitute $x = 22$ into the expression for $m\angle2$. $m\angle2=2x + 39=2\times22+39$. First, calculate $2\times22 = 44$, then $44+39 = 83$.

Answer:

$m\angle2 = 83^{\circ}$