imath - Graad 11 Wiskunde oefeninge i.v.m. hoeke in dieselfde segment in sirkels, Grade 11 Mathematics, more exercises re. angles in the same segment : antwoorde/answers.

WISKUNDE
GRAAD 10
NOG OEFENINGE

Hoeke in dieselfde segment : antwoorde

MATHEMATICS
GRADE 10
MORE EXERCISES

Angles in the same segment : answers.

   Antwoord / Answer 1.1

        2x = a  = 70°
          x = 35°
        2y =  (180° − a)
             =  (180° − 70°)
          y =  55°

     Vraag / Question 1.1

   Antwoord / Answer 1.2

          x = 2a  = 2 × 34°
             = 68°
        2y =  (180° − x)
             =  (180° − 68°)
          y =  56°

     Vraag / Question 1.2

   Antwoord / Answer 1.3

            x = a  = 40°
            y = 2a  = 2 × 40°
               =  80°
          2z =  (180° − y)  = (180° − 80°)
               =  100°
            z =  50°

     Vraag / Question 1.3

   Antwoord / Answer 1.4

        2x = 90°
          x = 45°
          x = y  = 45°
        2z =  (180° − 90°)
             =  90°
          z =  45°

     Vraag / Question 1.4

   Antwoord / Answer 1.5

             x = a  = 41°
             y = 2a  = 2 × 41°
               =  82°
           2z =  (360° − y)  = (360° − 82°)
                =  278°
             z =  139°

     Vraag / Question 1.5

   Antwoord / Answer 1.6

        2x = a
        2x = 150°
          x = 75°
          x = y  = 75°



     Vraag / Question 1.6

   Antwoord / Answer 1.7

             x = 2a  = 2 × 52°
               = 104°
             y = a  = 52°
             z = y  = 52°





     Vraag / Question 1.7

   Antwoord / Answer 1.8

        2x = a
        2x = 66°
          x = 33°
          y = x  = 33°
        2z = (360° − a)
             =  (360° − 66°:)
             =  294°
          z = 147°

     Vraag / Question 1.8

Antwoord / Answer 2

  2.1  ∠DOC = 2 × ∠DAC      . . .   midptshoek = 2 x omtrekshoek.  /  ∠ at centre = 2 x angle at circle
                        = 2 x 38°
                        = 76°

  2.2  ∠DBC = ∠DAC      . . .   omtreks∠^'e.  /  ∠^'s at circle
                       = 38°

  2.3  2 × ∠ODC = (180° − ∠DOC)      . . .   binnehoeke van ΔODC en OD = OC
                                                                           int. ∠'s of ΔODC and OD = OC
                             = (180° − 76°)
                             = 104°
                ∠ODC = 52°

  2.4  ∠BAC = ∠BDC      . . .   omtreks∠^'e.  /  ∠^'s at circle
                       = 66°


Vraag / Question 2

Antwoord / Answer 3

  3.1  ∠A = ∠OCA      . . .   OC = OA
                 = 28°

  3.2  ∠ACB = 90°      . . .   ∠ in halwe sirkel  /  ∠ in semi-circle

  3.3  ∠B = (180° − (∠BCA + ∠A))      . . .   binnehoeke van ΔABC  /  int. ∠'s of ΔABC
                 = (180° − (90° + 28°)
                 = 62°


Vraag / Question 3

Antwoord / Answer 4

  4.1  ∠N = ∠KML      . . .   omtreks∠^'e.  /  ∠^'s at circle
                 = 72°

  4.2  ∠KOL = 2 × ∠KML      . . .   midptshoek = 2 x omtrekshoek.  /  ∠ at centre = 2 x angle at circle
                     = 2 × 72°
                     = 144°

  4.3  ∠BML = ∠MKN      . . .   omtreks∠^'e.  /  ∠^'s at circle
                      = 30°


Vraag / Question 4

Antwoord / Answer 5

  5.1  ∠CAB = ∠CDB      . . .   omtreks∠^'e.  /  ∠^'s at circle
                       = 25°

  5.2  ∠ABD = ∠BEC &Nbsp;−  ∠BAC      . . .   buitehoek van ΔABE  /  ext. ∠ of ΔABE
                       =  130° − 25°
                       = 105°

  5.3  ∠AOD = 2 × ∠ABD      . . .   midptshoek = 2 x omtrekshoek.  /  ∠ at centre = 2 x angle at circle
                      = 2 × 105°
                      = 210°


Vraag / Question 5

Na bo