Question

4. In the diagram shown to the right, m∠GAF = x-6, m∠EAF = x +18, and m∠GAE = 72°. Find the value of x and the numerical values of m∠GAF and m∠EAF.

Answer 1

The joined angles are equal to 72 degrees, thefore the sum of GAF and FAE must be equal to that:

`\measuredangle GAF+\measuredangle FAE=72\degree`
`\begin{gathered} x+18+(x-6)=72 \\ 2x+18-6=72 \\ 2x+12=72 \\ 2x=72-12 \\ 2x=60 \\ x=(60)/(2)=30 \end{gathered}`

The values of GAF and FAE.

`\begin{gathered} \measuredangle GAF\text{ = x-6 = 30-6=24} \\ \measuredangle FAE=x+18=30+18=48 \end{gathered}`