biswash0987654321
biswash0987654321 biswash0987654321
  • 21-06-2020
  • Mathematics
contestada

In the given figure, angle ABC is an equilateral triangle. If AB//CE, prove that angle ACE = angle ECD​

In the given figure angle ABC is an equilateral triangle If ABCE prove that angle ACE angle ECD class=

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ronhagrid310
ronhagrid310 ronhagrid310
  • 21-06-2020

Answer:

Step-by-step explanation:

Triangle ABC is an equilateral triangle, then:

=> angle ABC = angle BAC = angle  ACB = 60 deg

AB // CE, according to alternative interior pair of angles theorem:

=> angle ACE = angle BAC = angle ABC = 60 deg   (1)

B, C, and D are colinear, then:

angle ECD + angle ACE + angle ACB = 180 deg

=> angle ECD = 180 - angle ACE - angle ACB = 180 - 60 - 60 = 60 deg   (2)

From (1) and (2):

=>angle ACE = angle ECD = 60 deg

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