Subjects geometry

Angles P Q

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1. The problem asks for the angles of points $p$ and $q$ in figure 5.8 (a). 2. Since the figure is not provided, I will explain how to find angles $p$ and $q$ generally in a triangle or geometric figure. 3. Use the angle sum property of triangles: the sum of interior angles is always $180^\circ$. 4. If $p$ and $q$ are angles in a triangle with a third angle $r$, then: $$p + q + r = 180^\circ$$ 5. If any side lengths or other angle measures are given, use trigonometric rules such as the Law of Sines or Law of Cosines: - Law of Sines: $$\frac{a}{\sin p} = \frac{b}{\sin q} = \frac{c}{\sin r}$$ - Law of Cosines: $$c^2 = a^2 + b^2 - 2ab \cos r$$ 6. Without the figure or additional data, the exact values of $p$ and $q$ cannot be determined. 7. Please provide the figure or more information to calculate the angles precisely.