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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.

4 In The Diagram Shown To The Right MGAF X6 MEAF X 18 And MGAE 72 Find The Value Of X And The Numerical Values Of MGAF And MEAF class=

Sagot :

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

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

The values of GAF and FAE.

[tex]\begin{gathered} \measuredangle GAF\text{ = x-6 = 30-6=24} \\ \measuredangle FAE=x+18=30+18=48 \end{gathered}[/tex]

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