Answer:
[tex] x = 65 [/tex]
Step-by-step explanation:
A linear pair of angles is formed when two adjacent angles are supplementary, meaning they add up to 180 degrees and share a common side. In other words, the two angles form a straight line.
In this case: the angles [tex] (x - 16)^\circ [/tex] and [tex] 131^\circ [/tex] form a linear pair, they must be adjacent and add up to 180 degrees.
So, we can write the equation:
[tex] (x - 16)^\circ + 131^\circ = 180^\circ [/tex]
Now, we solve for [tex] x [/tex]:
[tex] x - 16 + 131 = 180 [/tex]
[tex] x + 115 = 180 [/tex]
[tex] x = 180 - 115 [/tex]
[tex] x = 65 [/tex]
Thus, the angle [tex] (x - 16)^\circ [/tex] is [tex] (65 - 16)^\circ = 49^\circ [/tex], and [tex] 131^\circ [/tex] form a linear pair.
