Question

PLEASE HELP ME QUICK

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, m∠ABP is ANSWER ° and m∠ABC is ANSWER°

Answer 1

• m∠ABP is 32°,
• m∠ABC is 64°.

Explanation:

According to the construction we have:

• BD = BE
• PD = PE
• BP - is common side of triangles BPD and BPE

It gives us:

• ΔPBD ≅ ΔPBE

Then, corresponding angles of congruent triangles are congruent:

• ∠DBP ≅ ∠EBP

So,

• ∠ABP ≅ ∠CBP ⇒ m∠ABP = 32°

Then,

• m∠ABC = m∠ABP + m∠CBP = 32° + 32° = 64°