A circle is described around the quadrilateral CDEF, the angle CDF = 80 °, the angle DEC = 30 °. What is the DCF angle?

In the quadrilateral CDEF, inscribed in a circle, the angles based on the same arc are equal, that is, <DFC = <DEC = 30 °. Consider a triangle DCF with <DFC = 30 °; a <DEC = 80 °.

Then you can define <DCF = 180 ° – <DFC – <DEC = 180 ° – 30 ° – 80 ° = 70 °.

Answer: <DCF = 70 °.



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