Question

which of the following statements are true about the picture? select those that apply
a the value of x is 8
b the value of x is 21

Explanation:

Step1: Use the property of supplementary angles

Since the two angles \((5x + 2)^{\circ}\) and \((16x+10)^{\circ}\) are supplementary (they form a linear - pair), their sum is \(180^{\circ}\). So, we have the equation \(5x + 2+16x + 10=180\).

Step2: Combine like terms

Combine the \(x\) - terms and the constant terms: \((5x+16x)+(2 + 10)=180\), which simplifies to \(21x+12 = 180\).

Step3: Isolate the variable term

Subtract \(12\) from both sides of the equation: \(21x+12-12=180 - 12\), so \(21x=168\).

Step4: Solve for \(x\)

Divide both sides by \(21\): \(x=\frac{168}{21}=8\).

Answer:

A. The value of \(x\) is \(8\)