To construct the quadrilateral MUST with the given measurements, follow these steps:

1. Draw a line segment MU with a length of 3.8 cm.

2. At point U, draw a line segment US with a length of 3 cm. This line should be perpendicular to MU.

3. From point U, measure and mark a distance of 5 cm along the line segment US. This point will be labeled as T.

4. From point U, measure and mark a distance of 3.7 cm along the line segment MU. This point will be labeled as T.

5. Draw a line segment TS connecting points T and S.

6. From point S, measure and mark a distance of 5.8 cm along the line segment TS. This point will be labeled as M.

7. Connect points M and U with a line segment.

Now, you have constructed the quadrilateral MUST with the given measurements.

1) Draw AB = 3.8 cm.

2) Make

∠

A

B

X

=

80

o

.

3) From B, set off BC = 3.4 cm.

4) With A as center and radius equal to 5 cm draw an arc.

5) With C as center and radius equal to 4.5 cm, draw another arc, cutting the previous arc at D.

6) Join AD and CD.

Thus, ABCD is the required quadrilateral.