Angles and Angle Measurement — Engineering Board Exam Practice Questions

16 free engineering board exam reviewer questions on Angles and Angle Measurement (Plane Geometry), each with the correct answer and a worked solution.

1. Convert 3200 mils to degrees. (One full revolution equals 6400 mils.)
2. Find the angle in mils subtended by a line 20 yards long at a distance of 4000 yards.
3. A surveyor measures an angle of 3° at a distance of 2 km. Find the arc length subtended, assuming a circular arc of radius 2 km.
4. Assuming the earth is a sphere of radius 6400 km, find the distance along a 4° arc at the equator.
5. The angle subtended by an arc is 15 arcminutes. If the radius of the circle is 60 cm, find the length of the arc.
6. Find the number of degrees in 5π/6 radians.
7. Convert 225° to radians.
8. A pendulum swings through an arc of 20 cm at the end of a 150 cm rod. Find the angle, in degrees, through which it swings.
9. Find the smaller angle between the hands of a clock at 10:10.
10. Two supplementary angles differ by 40°. Find the smaller angle.
11. Between 2 o'clock and 3 o'clock, after how many minutes past 2:00 do the hands of a clock coincide?
12. Find the smaller angle between the hands of a clock at 3:40.
13. The angles of a triangle are in the ratio 2:3:4. Find the smallest angle.
14. What is the smaller angle between the hour hand and the minute hand of a clock at 4:00?
15. Find the supplement of an angle of 118°.
16. Find the complement of an angle of 37°.