Vertically opposite angles worksheet - Free Printable

Let's solve each of the angle problems (g) through (l) step by step, using properties of angles formed by intersecting lines:

---

(g)

We are given:
- ∠A = 20°
- Lines AB and CD intersect at a point.
- Angles labeled: x, y, z

Step-by-step:

- The angle marked 20° is adjacent to angle z, and together they form a straight line → supplementary angles.
- So, z = 180° − 20° = 160°
- Angle y is vertically opposite to the 20° angle → vertical angles are equal.
- So, y = 20°

✔ Answer: ∠y = 20°

---

(h)

Given:
- One angle = 105°
- Lines AB and CD intersect.

We need to find ∠y

Step-by-step:

- The 105° angle and x are on a straight line → supplementary
- So, x = 180° − 105° = 75°
- Angle y is vertically opposite to the 105° angle → vertical angles are equal
- So, y = 105°

✔ Answer: ∠y = 105°

---

(i)

Given:
- One angle = 120°
- Lines AB and CD intersect
- We need to find ∠z

Step-by-step:

- The 120° angle and x are on a straight line → supplementary
- So, x = 180° − 120° = 60°
- Angle z is vertically opposite to the 120° angle → vertical angles are equal
- So, z = 120°

✔ Answer: ∠z = 120°

---

(j)

Given:
- One angle = 30°
- Lines AB and CD intersect
- We need to find ∠z

Step-by-step:

- The 30° angle and z are adjacent angles forming a straight line → supplementary
- So, z = 180° − 30° = 150°

✔ Answer: ∠z = 150°

---

(k)

Given:
- One angle = 55°
- Two lines intersect
- We need to find ∠z

Step-by-step:

- The 55° angle and z are vertically opposite → vertical angles are equal
- So, z = 55°

✔ Answer: ∠z = 55°

---

(l)

Given:
- One angle = 140°
- Lines intersect
- We need to find ∠y

Step-by-step:

- The 140° angle and y are adjacent angles on a straight line → supplementary
- So, y = 180° − 140° = 40°

✔ Answer: ∠y = 40°

---

✔ Final Answers:

| Problem | Answer |
|--------|--------|
| (g) | ∠y = 20° |
| (h) | ∠y = 105° |
| (i) | ∠z = 120° |
| (j) | ∠z = 150° |
| (k) | ∠z = 55° |
| (l) | ∠y = 40° |

---

🔍 Key Concepts Used:

- Vertical angles are equal (opposite angles formed by two intersecting lines).
- Adjacent angles on a straight line sum to 180° (supplementary).

Let me know if you'd like diagrams or explanations for any specific one!