Question

a. what kind of angle do central street and spring street make? b. valerie is driving down spring street heading east. she takes a left onto river street. what type of angle did she have to turn her car through? c. what is the angle measure valerie is turning her car when she takes the left turn?

Explanation:

Step1: Identify angle - relationship

The angles $(x + 8)^{\circ}$ and $(3x+12)^{\circ}$ are supplementary (linear - pair), so $(x + 8)+(3x + 12)=180$.

Step2: Simplify the equation

Combine like - terms: $x+3x+8 + 12=180$, which gives $4x+20 = 180$.

Step3: Solve for x

Subtract 20 from both sides: $4x=180 - 20=160$. Then divide both sides by 4, so $x = 40$.

Step4: Find the angle measure for the turn

We know from part b that the turn is a right - angle. But if we want to find the measure of the non - right angle related to the intersection of Spring St. and River St., we can use one of the angle expressions. Let's use $x + 8$. Substitute $x = 40$ into $x + 8$, we get $40+8=48^{\circ}$. The angle of the left - turn (the non - straight part of the intersection) is $90^{\circ}$.

Answer:

$90^{\circ}$