Angle sum property of a triangle

Sum of angles of a triangle is 180°

Here,

∠A + ∠B + ∠C = 180°   

For proof, please check Theorem 6.7

Let’s solve some examples

Show that sum of angles of the triangle is 180°

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°

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

= 40° + 120° + 20°

= 180°        

Show that sum of angles of the triangle is 180°

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

= 45° + 90° + 45°

= 180°        

Find the missing angle of following triangles

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

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

In ∆XYZ,

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

  20° + 90° + ∠Z  = 180°

   110° + ∠Z = 180°

   ∠Z = 180° − 110°

  ∠Z = 70°