Question

Find the value of X.
Please give me a correct answer.
If you do you'll get 50 points :)

Answer 1

x = 23°

Explanation:

The Alternate Interior Angles Theorem states that if two parallel lines are cut by a transversal, then the alternate interior angles are equal.

In the given diagram, EF and AC are parallel, and EB is the transversal that cuts these parallel lines.

Therefore, according to the Alternate Interior Angles Theorem, ∠FEB ≅ ∠ABE. This means that m∠ABE = 4x. (See the attached diagram).

Angles on a straight line sum to 180°. Therefore:

`\begin{aligned}m \angle DBA + m \angle ABE + m \angle EBF &= 180^(\circ)\\x + 4x + 65^(\circ) &= 180^(\circ)\\5x + 65^(\circ) &= 180^(\circ)\\5x + 65^(\circ) - 65^(\circ) &= 180^(\circ) - 65^(\circ)\\5x &= 115^(\circ)\\5x/ 5&=115^(\circ) / 5\\x&=23^(\circ)\end{aligned}`

Therefore, the value of x is 23°.