Question: (5) 80°
y
(6)
y
(7)
y
65°
(8)
y
215°
(5) graph: intersecting lines forming an X with the top angle marked 80° and the opposite bottom angle marked y, position_hint=top-left
(6) graph: intersecting lines forming an X with a right-angle square at the bottom angle and the top angle marked y, position_hint=center-left
(7) graph: two rays meeting at a point with a reflex angle marked y around the top and the interior angle marked 65°, position_hint=lower-left
(8) graph: two rays meeting at a point with a reflex angle marked 215° on the right and the remaining angle marked y on the left, position_hint=bottom-left
Can U help w this
1. **Problem Statement:**
We are given four angle problems involving intersecting lines and reflex angles. We need to find the value of $y$ in each case.
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2. **Key Concepts:**
- Vertically opposite angles are equal.
- Angles on a straight line sum to $180^\circ$.
- Reflex angle is the larger angle around a point, summing with the adjacent angle to $360^\circ$.
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3. **Problem (5):**
- Given: One angle is $80^\circ$ and the opposite angle is $y$.
- Vertically opposite angles are equal, so:
$$y = 80^\circ$$
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4. **Problem (6):**
- Given: Intersecting lines with a right angle ($90^\circ$) at the bottom and the top angle is $y$.
- Vertically opposite angles are equal, so:
$$y = 90^\circ$$
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5. **Problem (7):**
- Given: Two rays meet at a point with an interior angle $65^\circ$ and reflex angle $y$ around the top.
- The sum of the interior angle and reflex angle around a point is $360^\circ$.
$$y + 65^\circ = 360^\circ$$
$$y = 360^\circ - 65^\circ = 295^\circ$$
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6. **Problem (8):**
- Given: Reflex angle $215^\circ$ on the right and remaining angle $y$ on the left.
- Angles around a point sum to $360^\circ$.
$$y + 215^\circ = 360^\circ$$
$$y = 360^\circ - 215^\circ = 145^\circ$$
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**Final answers:**
- (5) $y = 80^\circ$
- (6) $y = 90^\circ$
- (7) $y = 295^\circ$
- (8) $y = 145^\circ$