College

In the diagram shown to the right:

\[ m\angle GAF = x - 6 \]
\[ m\angle EAF = x + 18 \]
\[ m\angle GAE = 72 \]

Find the value of \( x \) and the numerical values of \( m\angle GAF \) and \( m\angle EAF \).

Answer :

Final answer:

In the given geometry question, we used the property that the sum of angles of a triangle adds up to 180 degrees. After plugging in and solving the equation, we find that the value of x is 48. The measurement of angle GAF is 42 and the measurement of angle EAF is 66.

Explanation:

From the issue, it is clear that it's an angle properties question in geometry. Given that, the sum of angles of a triangle equals to 180 degrees:

Using this rule, the equation will be mGAF + mEAF + mGAE = 180. If we substitute the given values into the equation, it becomes x - 6 + x + 18 + 72 = 180. Solving this equation, we get 2x + 84 = 180.

First, subtract 84 from both sides to isolate 2x. This calculation gives 2x = 96. Then, divide both sides by 2 to find the value of x. This gives x = 48.

Now that we have the value of x, mGAF = x - 6 = 42 and mEAF = x + 18 = 66.

Learn more about Triangle Angle Sum

find x first 72-18+6=48

now make x=48

48-6=42

now x is 42

42+18=60

now x=60

Thnks!

|Brailiest!!!!!!!!!

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