Answer:
x= 70
Explanation:
This question needs an attachment; see attached
Given
ABD = 55
Required
Find x?
In the figure shown in the attachment, angle b and ABD are alternate interior angles;
From parallel and perpendicular line theorems; alternate interior angles are equal.
This implies that <b = 55
Also; when a rectangle is divided by two diagonals, the resulting triangles are isosceles triangles;
where 2 sides and 2 angles are equal;
This implies that <b = <c = 55
Sum of angles in a triangle = 180;
So,
<x + <b + <c = 55
x + 55 + 55 = 180
x + 110 = 180
Subtract 110 from both sides
x + 110 - 110 = 180 - 110
x = 180 - 110
x = 70