Sum of angles of a triangle is 180°

18.jpg

Here,

∠A + ∠B + ∠C = 180°   

For proof, please check Theorem 6.7 (link)

Let’s solve some examples

 

Show that sum of angles of the triangle is 180°

19.jpg

Sum of all angles of triangle = ∠A + ∠B + ∠C

= 30° + 80° + 70°

= 110° + 70°

= 180°        

 

Show that sum of angles of the triangle is 180°

20.jpg

Sum of all angles of triangle = ∠P + ∠Q + ∠R

= 40° + 120° + 20°

= 180°        

 

Show that sum of angles of the triangle is 180°

21.jpg

Sum of all angles of triangle = ∠X + ∠Y + ∠Z

= 45° + 90° + 45°

= 180°        

 

Find the missing angle of following triangles

22.jpg

In ∆ABC,

  ∠A + ∠B + ∠C = 180°               (Angle sum property of triangle)

  55° + 75° + ∠C = 180°

  130° + ∠C = 180°

  ∠C = 180°  − 130°

  ∠C = 50° 

 

Find the missing angle of following triangles

23.jpg

In ∆PQR,

  ∠P + ∠Q + ∠R = 180°       (Angle sum property of triangle)

  30° + ∠Q + 50° = 180°

    ∠Q + 80° = 180°

    ∠Q = 180°  − 80°

   ∠Q = 100° 

 

Find the missing angle of following triangles

24.jpg

In ∆XYZ,

  ∠X + ∠Y + ∠Z = 180°         (Angle sum property of triangle)

  20° + 90° + ∠Z  = 180°

   110° + ∠Z = 180°

   ∠Z = 180° − 110°

  ∠Z = 70°

 

  1. Chapter 6 Class 7 Triangle and its Properties
  2. Concept wise

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.