HARD LINES

25/08/2026

📐 ANGLES IN TRIANGLES – FIND THE VALUE OF x! 🔢

Can you solve all six triangle-angle problems using the Angle Sum Property and Linear Pair Property? 🤔

✨ Key Rules to Remember:
• Sum of angles of a triangle = 180°
• Interior Angle + Exterior Angle = 180°

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ICSE Mathematics Triangles Angles Geometry MathsTricks MathsRevision ExamPreparation StudyMaths Class10 MathsPractice Education LearnMaths sachingupta rupamgupta hardlines gurdaspur

24/08/2026

🔷 EQUATIONS ABOUT POLYGONS 🔷

Learn how to solve equations using the sum of interior angles of different polygons. 📐✏️

In this post, you will find solved examples based on:
🔺 Triangles
⬜ Quadrilaterals
⬠ Pentagons
⬡ Hexagons
🛑 Octagons
🔺 Isosceles Triangles

Step-by-step solutions make it easy to understand and solve similar questions.

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PositiveVibes

24/08/2026

📐 LINES & ANGLES | BUILD STRONG GEOMETRY CONCEPTS

Master the essential Angle Pairs formed by a Transversal and strengthen your understanding of parallel lines and geometry.

🔹 Corresponding Angles
🔹 Alternate Interior Angles
🔹 Consecutive Interior Angles
🔹 Alternate Exterior Angles
🔹 Vertical Angles
🔹 Linear Pair Angles

🎯 Remember:
When two lines are parallel, corresponding, alternate interior and alternate exterior angles are equal, while consecutive interior angles are supplementary (sum = 180°).

📚 Learn the concepts. Practice regularly. Perform with confidence.

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24/08/2026

📐 LINES & ANGLES | BUILD STRONG GEOMETRY CONCEPTS

Master the essential Angle Pairs formed by a Transversal and strengthen your understanding of parallel lines and geometry.

🔹 Corresponding Angles
🔹 Alternate Interior Angles
🔹 Consecutive Interior Angles
🔹 Alternate Exterior Angles
🔹 Vertical Angles
🔹 Linear Pair Angles

🎯 Remember:
When two lines are parallel, corresponding, alternate interior and alternate exterior angles are equal, while consecutive interior angles are supplementary (sum = 180°).

📚 Learn the concepts. Practice regularly. Perform with confidence.

🎓 HARDLINES INSTITUTE
Learn Smart • Score High

▶️ Subscribe to our YouTube Channel
🔴 Hardlines Institute

📸 Follow us on Instagram
🟣 Hardlines Institute

🔔 Subscribe • Follow • Learn • Practice • Succeed

ParallelLines Transversal AnglePairs MathsLearning StudySmart LearnSmartScoreHigh Class9Maths Class10Maths CBSE ICSE PSEB Gurdaspur Punjab

23/08/2026

https://youtu.be/zE4LnS_pniA?si=FcUCUFNUVfoRqFv5

🚀 RANKING IN REASONING | FORMULA + SHORTCUTS + EXAMPLES

Master Ranking & Order Reasoning with easy formulas, smart shortcuts, and quick-solving tricks! 📚🧠

In this video, you will learn:
✅ Ranking formulas & basic concepts
✅ Position from left/right and top/bottom
✅ Finding total number of persons
✅ Finding rank/position of a person
✅ Important shortcuts for competitive exams
✅ Easy examples with step-by-step solutions

🎯 Useful for: Sainik School, RMS, Navodaya Vidyalaya, SSC, Railway, Banking, Police, and other competitive exams.

📌 Watch till the end and strengthen your Reasoning basics.
👍 Like | 💬 Comment | 🔔 Subscribe for more practice questions and shortcuts.





#2027




https://youtu.be/zE4LnS_pniA?si=FcUCUFNUVfoRqFv5

📚 Ranking & Order – Reasoning for Competitive ExamsWelcome to HAR...

23/08/2026

📐 **ANGLE RELATIONSHIPS – MASTER THE BASICS!** 🎯

Understanding angle relationships is the key to solving geometry questions quickly and confidently! 💯

This practice chart covers **12 important angle concepts**, including:

✅ Complementary Angles
✅ Supplementary Angles
✅ Vertically Opposite Angles
✅ Angles Between Parallel Lines
✅ Corresponding Angles
✅ Exterior Angle of a Triangle
✅ Adjacent Angles on a Straight Line
✅ Angle Bisector
✅ Sum of Angles of a Triangle
✅ Interior & Exterior Adjacent Angles
✅ Angles on a Straight Line
✅ Isosceles Triangle – Equal Base Angles

📚 **Master the Basics → Practice Regularly → Excel in Exams!**

🎓 Perfect for students preparing for **Sainik School | RMS | Navodaya | SSC | Railway | Banking | Other Competitive Exams**

📌 **Save this post** for quick revision!
❤️ Like | 💬 Comment | 📤 Share with your study partner

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📍 Gurdaspur
📲 Follow: **Hardlines Institute**

MathsShortcuts MathsPractice MathsRevision SainikSchool RMS NavodayaVidyalaya SSC RailwayExam BankingExam CompetitiveExams StudyTips MathsForStudents LearnPracticeExcel Gurdaspur

22/08/2026

📐 **ANGLE RELATIONSHIPS – MASTER THE BASICS!** 🎯

Understanding angle relationships is the key to solving geometry questions quickly and confidently! 💯

This practice chart covers **12 important angle concepts**, including:

✅ Complementary Angles
✅ Supplementary Angles
✅ Vertically Opposite Angles
✅ Angles Between Parallel Lines
✅ Corresponding Angles
✅ Exterior Angle of a Triangle
✅ Adjacent Angles on a Straight Line
✅ Angle Bisector
✅ Sum of Angles of a Triangle
✅ Interior & Exterior Adjacent Angles
✅ Angles on a Straight Line
✅ Isosceles Triangle – Equal Base Angles

📚 **Master the Basics → Practice Regularly → Excel in Exams!**

🎓 Perfect for students preparing for **Sainik School | RMS | Navodaya | SSC | Railway | Banking | Other Competitive Exams**

📌 **Save this post** for quick revision!
❤️ Like | 💬 Comment | 📤 Share with your study partner

🏫 **Hardlines Institute**
📍 Gurdaspur
📲 Follow: ****


Sachin Gupta PositiveVibes Rupam Gupta

21/08/2026

Writing
Percentage Formula & Shortcuts 📚✨
📌 MASTER PERCENTAGE IN MATH!
Percentage is one of the most important topics for Sainik School, Navodaya Vidyalaya, RMS, SSC, Railway, Banking & other competitive exams. 🎯
🔹 Basic Formula:
Percentage = (Part ÷ Whole) × 100
🔹 Find Percentage of a Number:
x% of y = (x × y) ÷ 100
🔹 Percentage Increase:
Increase % = (Increase ÷ Original Value) × 100
🔹 Percentage Decrease:
Decrease % = (Decrease ÷ Original Value) × 100
⚡ Quick Shortcut:
10% = ÷10
5% = ÷20
25% = ÷4
50% = ÷2
75% = ×3/4
💡 Tip: Learn the formulas + practice shortcuts regularly to solve questions faster and improve your exam accuracy.
🎯 Save this post for revision!
❤️ Like | 💬 Comment | 📲 Share | 🔔 Follow for more Maths Tricks & Practice Questions.
BasicMaths MathsQuestions MathsPreparation SainikSchool SainikSchoolExam Navodaya NavodayaVidyalaya RMS RMSExam CompetitiveExams EntranceExam Class6Maths MathsForStudents ExamPreparation StudyTips MathsRevision HardlinesInstitute

21/08/2026

https://youtu.be/VEOAdzyugSg?si=CCD_U6mnbce__If1

📚 SAINIK SCHOOL | RMS | NAVODAYA CLASS 6 ENTRANCE EXAM 2027Welco...