Question

the lines on a tennis court form adjacent angles with measures of (3a - 27)° and (2b + 14)°. find the values for a and b so that the lines are perpendicular. round to the nearest whole number if needed.

Explanation:

Step1: Recall perpendicular - angle property

When two lines are perpendicular, the adjacent angles formed are right - angles, so $(3a - 27)^{\circ}=90^{\circ}$ and $(2b + 14)^{\circ}=90^{\circ}$.

Step2: Solve for a

Solve the equation $3a-27 = 90$.
Add 27 to both sides: $3a=90 + 27=117$.
Divide both sides by 3: $a=\frac{117}{3}=39$.

Step3: Solve for b

Solve the equation $2b + 14=90$.
Subtract 14 from both sides: $2b=90 - 14 = 76$.
Divide both sides by 2: $b=\frac{76}{2}=38$.

Answer:

$a = 39$
$b = 38$