Question

Can someone please help me

Answer 1

Answer:

The value of x is 7

AC congruent to DF because AC = 13.5 in. and DF = 13.5 in, EF congruent to BC because EF = 12 in. and BC = 12 in., ∠C congruent to ∠F. The triangles ACB and DEF congruent by the SAS Triangle Congruence Theorem only when x = 7

Step-by-step explanation:

If two sides in a triangle congruent to two sides in other triangle and the including angles between the two sides are congruent in the triangles, then the two triangles are congruent by the SAS postulate of congruency

In the given figure

→ If ∠C ≅ ∠F

∵ m∠C = m∠F

∵ m ∠ C = (2x + 14)°

∵ m∠F = (4x)°

→ Equate them to find x

∴ 4x = 2x + 14

→ Subtract 2x from both sides

∴ 2x = 14

→ Divide both sides by 2

∴ x = 7

→ In Δs ABC and DEF

∵ AC congruent to DF because AC = 13.5 in. and DF = 13.5 in

∵ EF congruent to CB because EF = 12 in. and CB = 12 in.

∵ ∠C congruent to ∠F

∴ The triangles ACB and DEF congruent by the SAS Triangle Congruence

   Theorem only when x = 7