Certainly! Let's find the value of \(\( x \)\) step-by-step given the angles \(\( 40^\circ \)\) and \(\( (5x + 14)^\circ \)\).
1. Recognizing Supplementary Angles: The problem states that \(\( 40^\circ \)\) and \(\( (5x + 14)^\circ \)\) are angles on a straight line. Angles on a straight line are supplementary, which means their sum is \(\( 180^\circ \)\).
2. Setting Up the Equation: Since the angles sum to \(\( 180^\circ \)\), we can write the equation:
\(\[
40 + (5x + 14) = 180
\]\)
3. Simplifying the Equation: Start by removing the parentheses and combining the constants:
\(\[
40 + 5x + 14 = 180
\]\)
\(\[
54 + 5x = 180
\]\)
4. Isolating the Variable \(\( x \)\): Subtract \(\( 54 \)\) from both sides to isolate the term with \(\( x \)\):
\(\[
5x = 180 - 54
\]\)
\(\[
5x = 126
\]\)
5. Solving for \(\( x \)\): Finally, divide both sides by \(\( 5 \)\) to solve for \(\( x \)\):
\(\[
x = \frac{126}{5}
\]\)
\(\[
x = 25.2
\]\)
Thus, the value of \(\( x \)\) is \(\( 25.2 \)\).
