In the diagram, $PQR$ is a straight line.  What is the value of $x$?

[asy]
draw((-2,0)--(8,0),linewidth(0.7)); draw((8,0)--(5,-5.5)--(0,0),linewidth(0.7));
label("$P$",(-2,0),W); label("$Q$",(0,0),N); label("$R$",(8,0),E); label("$S$",(5,-5.5),S);

label("$136^\circ$",(0,0),SW); label("$64^\circ$",(7,0),S);

label("$x^\circ$",(5,-4.5));

[/asy]
Since $\angle PQS$ is an exterior angle of $\triangle QRS$, then $\angle PQS=\angle QRS+\angle QSR$, so $136^\circ = x^\circ + 64^\circ$ or $x = 136-64=\boxed{72}$.
72
Level 2
Prealgebra
Problem: In the diagram, $PQR$ is a straight line.  What is the value of $x$?

[asy]
draw((-2,0)--(8,0),linewidth(0.7)); draw((8,0)--(5,-5.5)--(0,0),linewidth(0.7));
label("$P$",(-2,0),W); label("$Q$",(0,0),N); label("$R$",(8,0),E); label("$S$",(5,-5.5),S);

label("$136^\circ$",(0,0),SW); label("$64^\circ$",(7,0),S);

label("$x^\circ$",(5,-4.5));

[/asy]
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the value of \( x \), we need to apply the properties of angles on a straight line. The angles \( 136^\circ \) and \( 64^\circ \) are adjacent to each other and together with \( x \) form a straight line at point \( Q \). 

According to the linear pair postulate, the sum of the angles on a straight line is \( 180^\circ \). Therefore, we can set up the equation:

\[
136^\circ + 64^\circ + x = 180^\circ
\]

First, we calculate the sum of \( 136^\circ \) and \( 64^\circ \):

\[
136^\circ + 64^\circ = 200^\circ
\]

Next, we substitute this sum back into the equation:

\[
200^\circ + x = 180^\circ
\]

To isolate \( x \), we subtract \( 200^\circ \) from both sides:

\[
x = 180^\circ - 200^\circ
\]

This simplifies to:

\[
x = -20^\circ
\]

However, since \( x \) represents an angle, it cannot be negative. This indicates that the angles \( 136^\circ \) and \( 64^\circ \) must be considered in a different context. 

Instead, we should recognize that \( x \) is the angle at point \( S \) that complements the angles at \( Q \) to maintain the straight line. Thus, we need to consider the angle \( x \) as the external angle formed by extending line \( QR \).

To find \( x \), we can use the fact that the external angle \( x \) is equal to the sum of the two non-adjacent interior angles:

\[
x = 136^\circ - 64^\circ
\]

Calculating this gives:

\[
x = 72^\circ
\]

Thus, the final answer is \( 72 \).<|END_OF_LATENT|> The final answer is $72$.