Problem

Use this algebraic congruence information to solve for the variable and name the congruence criterion: \(\angle~C~=~4x~+~8\), \(\angle~F~=~40\), \(BC~=~EF\), and angle \(B\) is congruent to angle \(E\).

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Set the corresponding angles equal: 4x + 8 = 40, so x = 8, and with ∠C ≅ ∠F, BC = EF, and ∠B ≅ ∠E, the triangles are congruent by AAS.

Set the corresponding angles equal: 4x + 8 = 40, so x = 8, and with ∠C ≅ ∠F, BC = EF, and ∠B ≅ ∠E, the triangles are congruent by ASA.

Set the corresponding angles equal: 4x + 8 = 40, so x = 12, and with ∠C ≅ ∠F, BC = EF, and ∠B ≅ ∠E, the triangles are congruent by ASA.

Set the corresponding angles equal: 4x + 8 = 40, so x = 8, and with BC = EF and the angle pairs congruent, the triangles are congruent by SAS.

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