Question

Please help me with this question. ​

Answer 1

x = 71

Explanation:

BE = BC , therefore Δ BCE is isosceles with 2 base angle congruent

∠ BEC = ∠ BCE =
`(180-38)/(2)` =
`(142)/(2)` = 71°

∠ ABE and ∠ BEF are alternate angles and are congruent , so

∠ BEF = 142°

∠ BEC + ∠ FEC = ∠ BEF , that is

71° + x = 142 ( subtract 71° from both sides )

x = 71

Answer 2

• x = 71°

Explanation:

According to diagram we have:

• ∠ABE ≅ ∠BEF as alternate interior angles
• m∠ABE = m∠BEC + m∠BCE exterior angle is sum of non-adjacent interior angles
• m∠BEC = m∠BCE as opposite sides are marked as equal

From the above statements we get:

• m∠ABE = 2m∠BEC ⇒ 142° = 2m∠BEC ⇒ m∠BEC = 71°

And

• m∠BEF = m∠ABE
• x + m∠BEC = m∠ABE
• x + 71° = 142°
• x = 71°