Geometry

Question Analysis:
This question assesses understanding of:
The Base Angles Theorem (angles opposite equal sides are congruent).
The Triangle Angle Sum Theorem (sum of interior angles = 180°).
Main Focus: Applying geometric theorems to find missing angles in an isosceles triangle.

Key Concept Explanation:
Isosceles Triangle Property: If two sides are congruent (PQ = PR), the angles opposite those sides (∠Q and ∠R) are congruent.
Triangle Angle Sum: All interior angles sum to 180°.

Step-by-Step Solution:
Identify congruent sides and angles:
Given PQ = PR, ∠Q and ∠R are congruent (Base Angles Theorem).
Assign angle measures:
∠Q = 34° ⇒ ∠R = 34° (since ∠Q ≅ ∠R).
Verify with Angle Sum Theorem:
∠P + ∠Q + ∠R = 180° ⇒ ∠P + 34° + 34° = 180° ⇒ ∠P = 112°.
(Note: This step confirms consistency but isn’t needed to answer the question.)

Common Mistakes:
Misapplying the Base Angles Theorem: Assuming ∠R is not equal to ∠Q because of the figure’s orientation.
Overcomplicating the solut...