Question

Ray EH bisects ∠FEG, m∠FEH = 4x - 21, and m∠GEH = 7x - 63. Find x and the

measures of ∠FEH and ∠GEH.

Answer 1

x = 14 , ∠ FEH = ∠ GEH = 35°

Explanation:

since EH bisects ( divides angle into 2 equal parts ) , then

∠ GEH = ∠ FEH ( substitute values )

7x - 63 = 4x - 21 ( subtract 4x from both sides )

7x - 4x - 63 = 4x - 4x - 21 ( simplify both sides )

3x - 63 = - 21 ( add 63 to both sides )

3x - 63 + 63 = - 21 + 63 ( simplify both sides )

3x = 42 ( divide both sides by 3 )

`(3)/(3)` x =
`(42)/(3)` , that is

x = 14

Then

∠ FEH = 4x - 21 = 4(14) - 21 = 56 - 21 = 35°

∠ GEH = 7x - 63 = 7(14) - 63 = 98 - 63 = 35°