Question: DRILL & PRACTICE Mathematics Year 5 PRACTICE 2 Find the unknown angles marked with ‘y’. Show your working steps in the spaces provided. (1) 156° y position_hint: top-left; graph: three rays meet at one point: one ray goes up, one goes left, and one goes down-right, with the 156° angle between the up ray and the down-right ray and y at the lower angle. (2) 168° 171° y position_hint: center-left; graph: three rays meet at one point: one ray goes left, one goes up-right, and one goes down-right, with 168° on the upper-left angle, 171° on the lower angle, and y on the right angle. (3) 30° 46° 107° y position_hint: center-left; graph: four rays meet at one point: one ray goes upper-left, one goes upper-right, one goes right, and one goes lower-left, with 30° between upper-left and upper-right, 46° between upper-right and right, 107° between right and lower-left, and y on the left angle. (4) 60° 20° y position_hint: bottom-left; graph: four rays meet at one point: one ray goes left, one goes up-right, one goes down-right, and one goes down, with 60° between up-right and down-right, 20° between down-right and down, and y on the upper-left angle.Help withthis plss

1. **Problem 1:** Find $y$ when three rays meet at a point with angles $156^\circ$, $y$, and the third angle. 2. The sum of angles around a point is always $360^\circ$. 3. Using the formula: $$156^\circ + y + \text{third angle} = 360^\circ$$ 4. Since the three rays form a straight line with $156^\circ$ and $y$ adjacent, the third angle is $180^\circ$ (straight line). 5. So, $$156^\circ + y = 180^\circ$$ 6. Subtract $156^\circ$ from both sides: $$\cancel{156^\circ} + y = 180^\circ - \cancel{156^\circ}$$ 7. Simplify: $$y = 24^\circ$$ --- 1. **Problem 2:** Find $y$ given angles $168^\circ$, $171^\circ$, and $y$ around a point. 2. Sum of angles around a point is $360^\circ$. 3. Write equation: $$168^\circ + 171^\circ + y = 360^\circ$$ 4. Add known angles: $$339^\circ + y = 360^\circ$$ 5. Subtract $339^\circ$ from both sides: $$\cancel{339^\circ} + y = 360^\circ - \cancel{339^\circ}$$ 6. Simplify: $$y = 21^\circ$$ --- 1. **Problem 3:** Find $y$ given four angles around a point: $30^\circ$, $46^\circ$, $107^\circ$, and $y$. 2. Sum of angles around a point is $360^\circ$. 3. Write equation: $$30^\circ + 46^\circ + 107^\circ + y = 360^\circ$$ 4. Add known angles: $$183^\circ + y = 360^\circ$$ 5. Subtract $183^\circ$ from both sides: $$\cancel{183^\circ} + y = 360^\circ - \cancel{183^\circ}$$ 6. Simplify: $$y = 177^\circ$$ --- 1. **Problem 4:** Find $y$ given four angles around a point: $60^\circ$, $20^\circ$, and $y$ plus one unknown angle. 2. Sum of angles around a point is $360^\circ$. 3. The unknown angle adjacent to $y$ and $60^\circ$ and $20^\circ$ is $y$'s supplementary angle. 4. Write equation: $$60^\circ + 20^\circ + y + \text{unknown angle} = 360^\circ$$ 5. Since the unknown angle and $y$ are adjacent and form a straight line, their sum is $180^\circ$: $$y + \text{unknown angle} = 180^\circ$$ 6. Substitute into total sum: $$60^\circ + 20^\circ + 180^\circ = 360^\circ$$ 7. Add: $$260^\circ = 360^\circ$$ 8. This is not possible unless $y$ and unknown angle sum to $180^\circ$ and the rest sum to $180^\circ$. 9. So, $y$ is supplementary to $60^\circ + 20^\circ = 80^\circ$: $$y = 180^\circ - 80^\circ = 100^\circ$$ --- **Final answers:** 1. $y = 24^\circ$ 2. $y = 21^\circ$ 3. $y = 177^\circ$ 4. $y = 100^\circ$