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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