What are the definitions of acute and straight angles, what is a straight line, and how to find x and construct angles?

The angles $x^\circ$ and $120^\circ$ are adjacent angles on a straight line AB. Angles on a straight line sum to $180^\circ$.

The value of x is $\boxed{60}$.

e) Construct the following angle by using compass and pencil:

*a) $90^\circ$

*b) $30^\circ$

a) Construction of $90^\circ$ angle:

1. Draw a ray OA.
2. With O as the center and a convenient radius, draw an arc that cuts OA at P.
3. With P as the center and the same radius, draw an arc that cuts the first arc at Q.
4. With Q as the center and the same radius, draw an arc that cuts the first arc at R.
5. With Q and R as centers and a radius greater than half of QR, draw two arcs that intersect each other at S.
6. Join OS. Angle AOS is $90^\circ$.

b) Construction of $30^\circ$ angle:

1. Draw a ray OA.
2. With O as the center and a convenient radius, draw an arc that cuts OA at P.
3. With P as the center and the same radius, draw an arc that cuts the first arc at Q. This creates a $60^\circ$ angle (angle AOQ).
4. With P and Q as centers and a radius greater than half of PQ, draw two arcs that intersect each other at R.
5. Join OR. Angle AOR is $30^\circ$.