End of chapter exercises

Calculate complementary and supplementary angles

1. Given line segment \(MN = 10 \text{ cm}\).

   1. Construct \(PQ\), the perpendicular bisector of \(MN\).
   2. Label point \(R\), the point of intersection of \(MN\) and \(PQ\).
   3. Measure and confirm that \(MR = RN\).

2. The diagrams below show the construction of a perpendicular bisector. The order of the diagrams is not correct. Study the diagrams and write down the correct order for constructing a perpendicular bisector of \(AB\).

   • Diagram 1
     
   • Diagram 2
     
   • Diagram 3
     
   • Diagram 4
     

3. Draw \(\triangle ABC\). Choose any length for the sides of \(\triangle ABC\).

   1. Construct the perpendicular bisector of \(AB\).
   2. Construct the perpendicular bisector of \(BC\).
   3. What do you notice about these two lines?
   4. Construct the perpendicular bisector of \(CA\).

4. Use a ruler and a compass to construct \(\triangle DEF\) with \(DE = 10 \text{ cm}\), \(EF = 8 \text{ cm}\) and \(FD = 6 \text{ cm}\).

5. Show that the sum of interior angles of a rectangle is \(360^{\circ}\).

6. Use a ruler and a compass to construct \(\triangle STU\) with \(ST = 5 \text{ cm}\), \(TU = 4 \text{ cm}\) and \(US = 3 \text{ cm}\).

7. Answer these questions about complementary and supplementary angles.

   1. What is the complement of \(28^{\circ}\)?
   2. What is the complement of \(70^{\circ}\)?
   3. What is the supplement of \(62^{\circ}\)?
   4. What is the supplement of \(103^{\circ}\)?

8. Use a ruler and a compass to construct equilateral \(\triangle ABC\) with \(AB = 7 \text{ cm}\).

9. Use a compass and a ruler to construct square \(JKLM\) with \(JK = \text{6,5} \text{ cm}\).

10. Show that the sum of interior angles of a square is \(360^{\circ}\).

11. In quadrilateral \(QRST\) below, \(\hat{Q} = 84^{\circ}, \hat{S} = 105^{\circ}\) and \(\hat{T} = 65^{\circ}\). Determine the value of \(x\), giving a reason for your answer.

    

12. In quadrilateral \(QRST\)is given. \(\hat{R} = 212^{\circ}, \hat{S} = 50^{\circ}\) and \(\hat{T} = 48^{\circ}\). Find the value of \(x\), giving a reason for your answer.