Question

I need help on this question

Answer 1

The diagram is represented below

We were told to find angle GCE. I have represented angle GCE as y.

Angles DCF and FCE make up a straight line. Sum of angles on a straight line = 180 degrees.

That means angle DCF + angle FCE = 180

therefore,

`\begin{gathered} 2x\text{ + 5 +3x - 20 = 180} \\ 2x\text{ + 3x + 5 - 20 = 180} \\ 5x\text{ - 15 = 180 } \\ 5x\text{ = 180 + 15} \\ 5x\text{ = 195 } \\ (5x)/(5)\text{ = }(195)/(5) \\ x=39^o \end{gathered}`

Now we have found the value for x, let us find angle GCE

Note that angle GCE is vertically opposite to angle DCF. Also vertically opposite angles are equal. Therefore DCF = GCE

GCE = DCF

y = DCF

y = 2x + 5

y = 2(39) + 5

y = 78 + 5 = 83 degrees.

Therefore, angle GCE = 83 degrees