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°
