Learning Resources

Investigation 4: Angles and Arcs

Test yourself (solution)

1.  Since  m= 96°, m Ð DFE = 48° (inscribed angle half the intercepted arc).  

2.  m Ð FDE +  mÐ FED = 180° - 48° = 132° (the sum of the angles of a triangle is 180°)

3.  Since DF = EF,   D DEF is isosceles. Therefore, m Ð FDE =  mÐ FED. 

4.  mÐ FED = ½ (132°) = 66°, therefore m = 132°.

5.  m = 180° (semi-circle)

6.  m = m - m = 180°-132° = 48°.

7.  mÐ CDF = ½ (m) = ½ (48°) = 24° 

8.  mÐ CEF = mÐCDF = 24° (inscribed angles intercepting the same arc )

9.  m=  m  - m = 180° - 96° = 84°

10.  mÐ CDE = ½ (m) = ½ (84°) = 42° (inscribed angle half the intercepted
       arc)