Question

angles a and b are supplementary. if a = 2x + 10 and b = 3x - 20, what is the value of x?

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to $180^{\circ}$. So, $A + B=180$.

Step2: Substitute the expressions for A and B

$(2x + 10)+(3x - 20)=180$.

Step3: Combine like - terms

$2x+3x+10 - 20=180$, which simplifies to $5x-10 = 180$.

Step4: Add 10 to both sides

$5x-10 + 10=180 + 10$, resulting in $5x=190$.

Step5: Divide both sides by 5

$\frac{5x}{5}=\frac{190}{5}$, so $x = 38$.

Answer:

$x = 38$