Angles of quadrilaterals - Wiki

  • #angleofquadrilaterals
    • In the figure below, ABCD is a rhombus. `/_`ABC `= 102^o` and `/_`CAE `= 19^o`. Find `/_`EAB. Ans: _BLANK_`^o`
      • #angleofquadrilaterals

        Triangle BAC is an isosceles triangle.

        < BAC = (180o - 102o`-:` 2 = 78o `-:` 2 = 39o 

        < EAB = 39o - 19o = 20o

  • #anglesofquadrilaterals
    • In the figure below, a rectangular piece of paper is folded along AD as shown. Given that EFBC is a straight line, find (a) `/_`EDF. (b) `/_`DFC. Ans: (a) _BLANK_ [2] Ans: (b) _BLANK_ [1]
      • #anglesofquadrilaterals

        (part a):

        `/_` BDA= 180o - 90o - 70o = 20o 

         `/_` EDF = 90o - 20o - 20o = 50

          (part b)

        `/_` DFE = 180o - 90o - 50o = 40o

        `/_` DFC = 180o - 40o = 140o
            

    • In the diagram below, ACF is a right-angled triangle, DEGH is a square and ABDH is a rhombus. Given that AB `=` BH, find `/_`AFC. Ans: _BLANK_`^o` [4]
      • #anglesofquadrilaterals

        ABDH is a rhombus, hence, triangle ABH and triangle BDH are equilateral triangles

        `/_` AHG = 360o - 60o - 60o - 90o = 150o 

        Triangle AGH is an isosceles triangle,

        `/_` HAG = (180o - 150o`-:` 2 = 15o 

        `/_` BAG = 60o + 15o = 75o 

        `/_` AFC = 180o - 90o - 75o = 15o