mwms2018sg
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  • 25-07-2020
  • Mathematics
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Angle bisectors AX and of triangle ABC meet at point I. Find angle C in degrees, if AIB = 109.

Angle bisectors AX and of triangle ABC meet at point I Find angle C in degrees if AIB 109 class=

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mathmate
mathmate mathmate
  • 25-07-2020

Answer:

angle C = 38 degrees

Step-by-step explanation:

Refer to attached figure (sorry, forgot to attach earlier)

Given

AIB = 109

Let

CAX = XAB = x

CBY = YBA = y

XIB = YIA = x+y    ........exterior angles

XIB = YIA = 180-109 = 71   ............ sum of angles on a line

=>

x+y = 71

ACB = 180 - 2x -2y  ................. sum of angles of a triangle

= 180 - 2(x+y)

= 180 - 2(71)

= 180 - 142

= 38

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