∠₁ + ∠₂ + ∠₃ + ∠₄ = 360° for angles around a point
∠₁ + ∠₂ = 180° for angles on a straight line
∠₁ + ∠₂ + ∠₃ = 180° for angles ∈ a triangle
sum of interior angles of a polygon = (n-2) × 180°
sum of exterior angles of a polygon = 360°
∠₁ = ∠₂ if two lines are ∥
∠₁ + ∠₂ = 180° if two lines are ∥ and a transversal intersects them
corresponding angles are equal if two lines are ∥ and a transversal intersects them

🪤 The 5 Mistakes That Cost Marks

Forgetting that vertically opposite angles are equal
Not checking if lines are ∥ before applying properties of ∥ lines
Not applying the property that sum of interior angles of a triangle is 180°
Confusing corresponding angles with alternate interior angles
Not using the property that sum of interior angles of a polygon is (n-2) × 180°

✏️ 3 Solved PYQs

In a triangle, the sum of two angles is 90°. If the third angle is 30°, find the other two angles. Step 1: Let the two angles be ∠₁ and ∠₂. Step 2: We know that ∠₁ + ∠₂ + ∠₃ = 180°. Step 3: Given ∠₃ = 30° and ∠₁ + ∠₂ = 90°. Step 4: Substitute the values ∈ the equation ∠₁ + ∠₂ + ∠₃ = 180°. Step 5: We get 90° + 30° = 120°. Step 6: The other two angles are 60° and 30°.
Two lines intersect at a point. If one of the angles formed is 45°, find the other three angles. Step 1: Let the four angles be ∠₁, ∠₂, ∠₃, and ∠₄. Step 2: We know that ∠₁ + ∠₂ + ∠₃ + ∠₄ = 360°. Step 3: Also, ∠₁ + ∠₂ = 180°, ∠₃ + ∠₄ = 180°, and ∠₁ + ∠₃ = 180°. Step 4: Given ∠₁ = 45°. Step 5: We can find ∠₂ = 180° - ∠₁ = 135°. Step 6: Similarly, ∠₃ = 180° - ∠₁ = 135° and ∠₄ = 180° - ∠₃ = 45°.
In a quadrilateral, three angles are 80°, 100°, and 120°. Find the fourth angle. Step 1: Let the four angles be ∠₁, ∠₂, ∠₃, and ∠₄. Step 2: We know that ∠₁ + ∠₂ + ∠₃ + ∠₄ = 360°. Step 3: Given ∠₁ = 80°, ∠₂ = 100°, and ∠₃ = 120°. Step 4: Substitute the values ∈ the equation ∠₁ + ∠₂ + ∠₃ + ∠₄ = 360°. Step 5: We get 80° + 100° + 120° + ∠₄ = 360°. Step 6: Simplifying, we get 300° + ∠₄ = 360°. Step 7: Therefore, ∠₄ = 60°.

🧠 The One Thing Most Students Get Wrong

Most students get confused between corresponding angles and alternate interior angles.
Corresponding angles are equal if two lines are ∥ and a transversal intersects them.
Alternate interior angles are equal if two lines are ∥ and a transversal intersects them.
However, corresponding angles and alternate interior angles are not the same thing.

👁️ Ayush's Note

Make sure to check if lines are ∥ before applying properties of ∥ lines.
Always use the property that sum of interior angles of a triangle is 180°.
Use the property that sum of interior angles of a polygon is (n-2) × 180° to find unknown angles.
Practice solving problems involving angles ∈ a triangle, quadrilateral, and polygon.

🔁 Last 5 Minutes Box

Go through the formula bank to recall important formulas.
Check if you have applied the properties of ∥ lines correctly.
Verify that you have used the correct property for sum of interior angles of a polygon.
Make sure to check your calculations for finding unknown angles.
Review the solved PYQs to recall the steps for solving problems.

📝 Practice MCQs

1. If two lines intersect at a point, then the sum of the four angles formed is

A) 180°

B) 270°

C) 360°

D) 450°

Answer: C) 360°.

2. If one of the angles formed by two intersecting lines is 60°, then the other three angles are

A) 60°, 120°, 120°

B) 60°, 60°, 120°

C) 60°, 120°, 60°

D) 120°, 120°, 60°

Answer: C) 60°, 120°, 60°.

3. In a triangle, the sum of two angles is 90°. If the third angle is 45°, find the other two angles.

A) 30°, 60°

B) 45°, 45°

C) 60°, 30°

D) 45°, 90°

Answer: B) 45°, 45°.

4. Two lines are ∥ if

A) corresponding angles are equal

B) alternate interior angles are equal

C) corresponding angles and alternate interior angles are equal

D) all of the above

Answer: D) all of the above.

5. In a quadrilateral, three angles are 80°, 100°, and 120°. Find the fourth angle.

A) 40°

B) 60°

C) 80°

D) 60°

Answer: B) 60°.

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📚 Academic References

Content verified against peer-reviewed research:

�Let the People Rap�: Cultural Rhetorics Pedagogy and Practices U... — Journal of Basic Writing (2019) 🔓 — DOI ↗
Frustration and Hope: Examining Students� Emotional Responses to ... — Journal of Basic Writing (2019) — DOI ↗
Editors' Column — Journal of Basic Writing (2019) — DOI ↗

🔓 = Open Access article

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This post was curated by Jules, Exam Compass Bot, and edited for accuracy by Ayush.

📚 Related Topics

Continue your revision with these related guides:

∠₁ + ∠₂ + ∠₃ + ∠₄ = 360° for angles around a point
∠₁ + ∠₂ = 180° for angles on a straight line
∠₁ + ∠₂ + ∠₃ = 180° for angles ∈ a triangle
sum of interior angles of a polygon = (n-2) × 180°
sum of exterior angles of a polygon = 360°
∠₁ = ∠₂ if two lines are ∥
∠₁ + ∠₂ = 180° if two lines are ∥ and a transversal intersects them
corresponding angles are equal if two lines are ∥ and a transversal intersects them