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Omni-MATH / Let ABC be a triangle, and let D,E, and F be the midpoints of sides BC,CA, and AB, respectively. Let the angle bisectors of ∠FDE and ∠FBD meet at P. Given that ∠BAC=37^(∘) and …

Problem

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problem

Let ABCA B C be a triangle, and let D,ED, E, and FF be the midpoints of sides BC,CAB C, C A, and ABA B, respectively. Let the angle bisectors of ∠FDE\angle F D E and ∠FBD\angle F B D meet at PP. Given that ∠BAC=37∘\angle B A C=37^{\circ} and ∠CBA=85∘\angle C B A=85^{\circ}, determine the degree measure of ∠BPD\angle B P D.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle, and let D,E, and F be the midpoints of sides BC,CA, and AB, respectively. Let the angle bisectors of ∠FDE and ∠FBD meet at P. Given that ∠BAC=37^(∘) and ∠CBA=85^(∘), determine the degree measure of ∠BPD.
Original LaTeX notation
Let $A B C$ be a triangle, and let $D, E$, and $F$ be the midpoints of sides $B C, C A$, and $A B$, respectively. Let the angle bisectors of $\angle F D E$ and $\angle F B D$ meet at $P$. Given that $\angle B A C=37^{\circ}$ and $\angle C B A=85^{\circ}$, determine the degree measure of $\angle B P D$.

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Source and history

task_id
6ebab918-1488-54c2-b08d-a241e530be4c
task_key
test--6ebab918-1488-54c2-b08d-a241e530be4c
task_revision_id
1
config / split
/ test

Official source

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