Question

In the diagram, points D and E are marked by drawing arcs of equal size centered at B such that the arcs intersect BA and BC . Then, intersecting arcs of equal size are drawn centered at points D and E. Point P is located at the intersection of these arcs. Based on this construction, ABP is ___
A. 32
B. 50
C. 64
D. 128

*this is on Plato, and the image wouldn't paste

Answer 1

The problem asks to find the measure of the angle ABC based on the diagram in the problem and where as point D and E are marked by drawing arcs of equal size center at B so the measure of the angle ABC is 64 degree. I hope you are satisfied with my answer and feel free to ask for more.

Answer 2

Based on the construction of the arcs and angles, it can be deduced that the measure of ∠ABC is 64° (Option C). See the proof of the same below.

What is the proof to the answer above?

Recall the following:

• The points D and E are marked using arcs of equal size from a common center B;

• Intersecting arcs of equal size are drawn centered at points D and E. Point P is situated at the intersection of these arcs.

What the above means is that Line BP divides the ∠ABC at equal ratios from point ABC.

Therefore, if the above is true, then the ∠PBE which is 32° must be equal to the ∠PBD.

Hence,

∠ABP = 32 * 2  = 64°

Learn more about angles at:

https://brainly.com/question/25770607

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