Question

1. solve for x. (x + 15)° (3x + 1)°

Explanation:

Step1: Identify supplementary angles

The two angles \((x + 15)^\circ\) and \((3x + 1)^\circ\) are supplementary (they form a linear pair), so their sum is \(180^\circ\).
\[
(x + 15) + (3x + 1) = 180
\]

Step2: Combine like terms

Combine the \(x\) terms and the constant terms.
\[
x + 3x + 15 + 1 = 180 \\
4x + 16 = 180
\]

Step3: Subtract 16 from both sides

\[
4x + 16 - 16 = 180 - 16 \\
4x = 164
\]

Step4: Divide by 4

\[
\frac{4x}{4} = \frac{164}{4} \\
x = 41
\]

Answer:

\(x = 41\)