If the sides of KLM are produced to P,Q and R as shown, find the sum of exterior angles 1, 2 and 3.
Answers
Sum of all exterior angle is 360°.
Step-by-step explanation:
1. Given data
ΔKLM is a triangle, so
∠LKM+ ∠MLK+ ∠KML =180° (sum of triangle angle property)
∠LKM+ ∠MLK+ ∠KML =180° ...1)
2. ∠LKM and ∠1 is a linear pair angle along line LR. So
∠LKM + ∠1 = 180° ...2)
∠MLK and ∠2 is a linear pair angle along line PM. So
∠MLK + ∠2 = 180° ...3)
∠KML and ∠3 is a linear pair angle along line QK. So
∠KML + ∠3 = 180° ...4)
3. Adding equation 2) , equation 3) and equation 4). We get
∠LKM+ ∠MLK+ ∠KML+ ∠1+ ∠2+ ∠3 =180° +180° +180° ...5)
From equation 1) and equation 5)
180° + ∠1+ ∠2+ ∠3 =180° +180° +180°
So
∠1+ ∠2+ ∠3 =180° +180°
∠1+ ∠2+ ∠3 =360°
means sum of all exterior angle is 360°