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