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 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, and the sum of adjacent angles is 90 degrees. So we set up two equations:
$3a−27 = 90$ and $2b + 14=90$.

Step2: Solve for $a$

Add 27 to both sides of the equation $3a−27 = 90$:
$3a=90 + 27$
$3a=117$.
Then divide both sides by 3:
$a=\frac{117}{3}=39$.

Step3: Solve for $b$

Subtract 14 from both sides of the equation $2b + 14 = 90$:
$2b=90−14$
$2b = 76$.
Then divide both sides by 2:
$b=\frac{76}{2}=38$.

Answer:

$a = 39$
$b = 38$