Question

find the measure of each angle
3x + 1 = 66°
13x + 9 = 24°
(simplify your answers. type an integer or a fraction )

Explanation:

Step1: Note angle relationship

The two angles $3x + 1$ and $13x+9$ are complementary (since they form a right - angle, which is 90°), so $(3x + 1)+(13x + 9)=90$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $3x+13x+1 + 9=90$, which simplifies to $16x+10 = 90$.

Step3: Isolate the variable term

Subtract 10 from both sides: $16x=90 - 10$, so $16x=80$.

Step4: Solve for $x$

Divide both sides by 16: $x=\frac{80}{16}=5$.

Step5: Find the measure of the first angle

Substitute $x = 5$ into $3x + 1$: $3\times5+1=15 + 1=16$.

Step6: Find the measure of the second angle

Substitute $x = 5$ into $13x + 9$: $13\times5+9=65 + 9=74$.

Answer:

$3x + 1 = 16^{\circ}$
$13x + 9 = 74^{\circ}$