Question

the given lines are parallel. provide the value of x and the measure of the angles. (13x - 21)° (5x + 75)° 13x - 5x - 21 = 5x - 5x + 75 8x - 21 = 75 +21 +21 5x + 75 8x = 96 5x12 + 75 = 60 + 75 = 135 8/8 = 12 x = 12 135° (5x + 3)° (9x - 33)°

Explanation:

Step1: Set up equation

Since the lines are parallel, the corresponding angles are equal. So we set up the equation $5x + 3=9x - 33$.

Step2: Isolate x - terms

Subtract $5x$ from both sides: $5x+3 - 5x=9x - 33-5x$, which simplifies to $3 = 4x-33$.

Step3: Isolate the term with x

Add 33 to both sides: $3 + 33=4x-33 + 33$, getting $36 = 4x$.

Step4: Solve for x

Divide both sides by 4: $\frac{36}{4}=\frac{4x}{4}$, so $x = 9$.

Step5: Find angle measure

Substitute $x = 9$ into $5x + 3$: $5\times9+3=45 + 3=48$.

Answer:

$x = 9$, measure of the angles is $48^{\circ}$