Question

elm street, continental road, and jefferson avenue intersect at one point on the map shown. elm street and continental road are perpendicular to each other. if the measure of ∠2=(2x + 10)° and m∠3 = 40°, determine the value of x. your answer

Explanation:

Step1: Use perpendicular - angle property

Since Elm Street and Continental Road are perpendicular, $\angle1 = 90^{\circ}$. And $\angle1+\angle2+\angle3=180^{\circ}$ (a straight - line angle).

Step2: Substitute known values

Substitute $\angle1 = 90^{\circ}$ and $\angle3 = 40^{\circ}$ into $\angle1+\angle2+\angle3=180^{\circ}$. We get $90+(2x + 10)+40=180$.

Step3: Simplify the equation

First, combine like terms: $90 + 10+40+2x=180$, which simplifies to $140+2x=180$.

Step4: Solve for x

Subtract 140 from both sides of the equation: $2x=180 - 140$, so $2x = 40$. Then divide both sides by 2: $x=\frac{40}{2}=20$.

Answer:

$20$