Question

for the following intersection, the measurements of the indicated angles are represented by the expressions ∠a = (-2x + 61)° and ∠c = (x + 55)°. what are the numerical angle measurements of ∠a and ∠c?

Explanation:

Step1: Set up equation

Since $\angle a$ and $\angle c$ are vertical - angles, they are equal. So, $-2x + 61=x + 55$.

Step2: Solve for $x$

Add $2x$ to both sides: $61 = 3x+55$. Then subtract 55 from both sides: $3x=61 - 55=6$. Divide both sides by 3: $x = 2$.

Step3: Find $\angle a$

Substitute $x = 2$ into the expression for $\angle a$: $\angle a=-2\times2 + 61=-4 + 61 = 57^{\circ}$.

Step4: Find $\angle c$

Substitute $x = 2$ into the expression for $\angle c$: $\angle c=2 + 55=57^{\circ}$.

Answer:

$\angle a = 57^{\circ}$, $\angle c = 57^{\circ}$