Wednesday, 31 August 2016

Angles (Rhombus & Parallelogram)

In the figure below, ABCD is a rhombus and CDEF is a parallelogram, ∠ADE is 150° and ∠CFE is 115°. Find ∠x.





Method 1
FCB = 150° (corresponding angles)
FCD = 180° - 115° = 65° (co-interior angles of a parallelogram)
DCB = 150° - 65° = 85°
DAB = 85° (diagonally opposite angles of a rhombus)
∠x = 85° / 2 = 42.5° (angle bisector of a rhombus)

Method 2
EDC = 115° (diagonally opposite angles of a parallelogram)
CDA = 360° - 150° - 115° = 95° (angles at a point)
DAB = 180° - 95° = 85° (co-interior angles of a parallelogram)
∠x = 85° / 2 = 42.5° (angle bisector of a rhombus)

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