Question

If the sides of triangle KLM are produced to p, q and R as shown, find the sum of exterior angles, angle 1, angle 2, and angle 3​

Answer 1

Step-by-step explanation:

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Answer 2

$\\\angle 1 +\angle 2+\angle 3 = 360 ^\circ$

Step-by-step explanation:

here ,

$\angle 1 = \angle KLM + \angle KML\\\angle 2 = \angle LKM + \angle LMK\\ \angle 3 = \angle MKL + \angle MLK$

(exterior angle property)

adding the equations

we get

$\angle 1 +\angle 2+\angle 3 = 2(\angle LKM + \angle KML+\angle MLK)$

$(\angle LKM + \angle KML+\angle MLK)= 180^\circ$

(angle sum property)

then

$\angle 1 +\angle 2+\angle 3 = 2(180^\circ)\\\\\angle 1 +\angle 2+\angle 3 = 360 ^\circ$

hence ,

$\\\angle 1 +\angle 2+\angle 3 = 360 ^\circ$

#Learn more:

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