Question

if ∠a and ∠b are supplementary and ∠a = 5x - 7, ∠b = 3x + 15, what is the value of x? 18 19 20 21

Explanation:

Step1: Recall supplementary - angle property

$\angle A+\angle B = 180^{\circ}$

Step2: Substitute angle expressions

$(5x - 7)+(3x + 15)=180$

Step3: Combine like - terms

$5x+3x-7 + 15=180$
$8x + 8=180$

Step4: Isolate the variable term

$8x=180 - 8$
$8x=172$

Step5: Solve for x

$x=\frac{172}{8}=21.5$

It seems there is a mistake in the provided options as the correct value of $x$ is $21.5$. If we assume there was a rounding or a calculation error in the problem - setup and we consider the closest integer value among the options, we would choose 22.

Answer:

22