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, what is the measure of ∠ABC ?.

Answer 1

here are the answer choices
 m∠ABC=32°
 m∠ABC=64°
 m∠ABC=90°
 m∠ABC=128°

∠ ABC is less than 90° so the 3rd and 4th option is out.

The most likely answer is 64°. m∠ABC = 64°

32° x 2 = 64°

Answer 2

Answer:

Step-by-step explanation:

Alright , lets get started.

From point B, two arcs are formed, BE and BD.

From the point, E and D, two again arcs are made which are intersecting each other at point P.

It means, line BP is bisector of angle ABC.

$ABC = 2 * PBE$

$ABC = 2 * 32$

$ABC = 64$

Hence the angle ABC is 64 degrees.   :    Answer

Hope it will help :)