1. Problem 8(a): Two intersecting lines with angles 52°, 35°, and x. - Since vertical angles are equal, and the sum of angles around a point is 360°, we find $x$ by: $$x = 360° - (52° + 35° + 52° + 35°) = 360° - 174° = 186°$$ 2. Problem 8(b): Quadrilateral PQRS with angles 34° and y. - Sum of interior angles in a quadrilateral is 360°. - If other angles are known or implied, solve for $y$ accordingly. Without more info, assume $y = 360° - 34° - \text{other angles}$. 3. Problem 8(c): Two adjacent triangles PQR and RST with angles 84°, 56°, and x°. - Sum of angles in a triangle is 180°. - For triangle PQR: $x = 180° - 84° - 56° = 40°$ 4. Problem 8(d): Quadrilateral with diagonals intersecting at O, angle 50° at vertex S. - Without more info, angle at S is given as 50°. 5. Problem 8(e): Angles 52°, x, and 312° on connected lines. - Sum of angles around a point is 360°. - Calculate $x$: $$x = 360° - 52° - 312° = -4°$$ - Negative angle suggests recheck or angle outside normal range; possibly $x = 8°$ if 312° is reflex angle. 6. Problem 8(f): Triangle RST with angles 35°, x. - Sum of angles in triangle is 180°. - If third angle known, solve for $x$; else $x = 180° - 35° - \text{third angle}$. 7. Problem 9(a): Two adjacent angles 140°, 110° with unknown $x$ and $w$ in between. - Sum of angles on a straight line is 180°. - $x + 140° = 180° \Rightarrow x = 40°$ - $w + 110° = 180° \Rightarrow w = 70°$ 8. Problem 9(b): Circle with radius line showing $5y$, marked with 36° and $y$. - Central angle 36°, arc length proportional to $y$. - Without more info, $y$ remains symbolic. 9. Problem 9(c): Circle with 6 sectors labeled $2z$, $3z$, $2z$, $z$, and angle 108°. - Sum of central angles in circle is 360°. - Equation: $$2z + 3z + 2z + z + 108° = 360°$$ $$8z + 108° = 360°$$ $$8z = 252°$$ $$z = 31.5°$$ Final answers: - 8(a): $x = 186°$ - 8(c): $x = 40°$ - 9(a): $x = 40°$, $w = 70°$ - 9(c): $z = 31.5°$