A vertically opposite angle is a pair of angles formed due to the intersection of two lines, and are said to be equal. Thus the angle that is the same as <BPD is <APC.
ii. The value of x is [tex]47^{o}[/tex].
The intersection of two or more lines at a point will always produce a set of angles. Some of these angles when compared may have similar measures or properties.
Two angles can be equal with respect to their measure if they are vertically opposite. Vertically opposite angles are angles formed when two lines intersect, such that a pair of opposite angles about the point of intersection are equal.
Thus from the given question, the angle that is the same as <PBD is <APC.
i.e <BPD ≅ <APC (vertically opposite property)
Also,
x + 133 = 180 (sum of angles on a straight line)
x = 180 - 133
= 47
x = [tex]47^{o}[/tex]
Therefore the value of x is [tex]47^{o}[/tex].
For more clarifications on vertically opposite angles, visit: https://brainly.com/question/68367
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