Question

2. Sides BC, CA and AB of a triangle ABC are produced in an order,
forming exterior angles ACD, BAE and CBF. Show that
ACD+ BAE + CBF =360°.​

Answer 1

Question: Sides BC, CA and AB of a (equilateral) triangle ABC , produced in an order , forming exterior angles ACD , BAE and CBF . Show that ACD + BAE + CBF= 360°

Solution: Since ABC is an equilateral triangle.

So , all interior angles of an equilateral triangle = 60°

ACD + ACB = 180°. [ linear pair axiom]

ACD + 60° = 180°

=> ACD = (180 - 60)°

=> { ACD = 120° }

Similarly by linear pair ,

BAE and CBF = 120°

So, ACD + BAE + CBF = 120° +120° + 120°

=> ACD + BAE + CBF = 360°

Hence Proved.

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