Answer: x = 50
Concept:
Here, we need to know the idea of alternative interior angles and the angle sum theorem.
Alternative interior angles are angles that are formed inside the two parallel lines, and the values are equal.
The angle sum theorem implies that the sum of interior angles of a triangle is 180°
If you are still confused, please refer to the attachment below or let me know.
Explanation:
Given information:
AC ║ DE
∠ABC = 85°
∠A = 135°
Find the value of ∠BAC
∠A + ∠BAC = 180° (Supplementary angle)
(135°) + ∠BAC = 180°
∠BAC = 45°
Find the value of ∠BCA
∠ABC + ∠BAC + ∠BCA = 180° (Angle sum theorem)
(85°) + (45°) + ∠BCA = 180°
∠BCA = 50°
Find the value of x (∠EBC)
∠EBC ≅ ∠BCA (Alternative interior angles)
Since, ∠BCA = 50°
Therefore, ∠EBC = 50°
Hope this helps!! :)
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