Question

what is the measure of ∠3? 55 155 45 135

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle 3$ and the angle with measure $5x + 35^{\circ}$ are vertical angles. Also, the angle with measure $45^{\circ}$ and the angle with measure $5x+35^{\circ}$ are supplementary (linear - pair), so $45+(5x + 35)=180$.

Step2: Solve the equation for $x$

First, simplify the left - hand side of the equation: $45+5x + 35=180$, which gives $5x+80 = 180$. Then subtract 80 from both sides: $5x=180 - 80=100$. Divide both sides by 5: $x = 20$.

Step3: Find the measure of $\angle 3$

Since $\angle 3=5x + 35^{\circ}$ and $x = 20$, substitute $x$ into the expression: $\angle 3=5\times20+35=100 + 35=135^{\circ}$.

Answer:

$135$