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If the measure of angle EFG is [tex](5x + 1)[/tex] degrees, and the measure of angle HFG is [tex]62[/tex] degrees, and the measure of angle EFG is also given as [tex](18x + 11)[/tex] degrees, how do we find each measure?

Answer :

Final answer:

Due to a typographical error in the question, two methods are presented to solve for 'x' depending on the correct expression for m measure EFG. Each results in determining that EFG is 62 degrees, confirming that m measure HFG and m measure EFG are congruent.

Explanation:

There is a discrepancy in the question as it has given two different expressions for m measure EFG: (5x+1) degrees and (18x+11) degrees. Assuming this is a typographical error, and only one expression is correct, we can find the value of 'x' using the second given angle m measure HFG which is 62 degrees. Now, if m measure EFG is really (5x+1) degrees, then we set it equal to 62 degrees and solve for 'x':

  • 5x + 1 = 62
  • 5x = 61
  • x = 12.2

If the correct expression for m measure EFG is (18x+11) degrees, the following steps are taken:

  • 18x + 11 = 62
  • 18x = 51
  • x = 2.8333

In the case of (5x+1) degrees, we can calculate EFG using x = 12.2 to find that EFG is 62 degrees. If the correct expression is (18x+11) degrees, then with x = 2.8333, EFG = 62 degrees.

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