Question

In figure(1), AC I CE and ZA:ZB: 2C = 5:2:2,
find the measure of ZECD.

Answer 1

Let A, B and C be 3x, 2x and x respectively.

3x +2x +x = 180   (angle sum of )

6x = 180 x = 30

A = 90, B = 60 and ACB =30

Now, ACB + ACE + ECD = 180 (angles on a straight line)

30o + 90 + ECD = 180

ECD = 180 – 120= 60

Hence, ECD = 60

Answer 2

Step-by-step explanation:

Let A, B and C be 3x, 2x and x respectively.

Let A, B and C be 3x, 2x and x respectively.3x +2x +x = 180o (angle sum of )

Let A, B and C be 3x, 2x and x respectively.3x +2x +x = 180o (angle sum of )6x = 180o x = 30

Let A, B and C be 3x, 2x and x respectively.3x +2x +x = 180o (angle sum of )6x = 180o x = 30 A = 90o, B = 60o and ACB =30o

Let A, B and C be 3x, 2x and x respectively.3x +2x +x = 180o (angle sum of )6x = 180o x = 30 A = 90o, B = 60o and ACB =30oNow, ACB + ACE + ECD = 180o (angles on a straight line)

Let A, B and C be 3x, 2x and x respectively.3x +2x +x = 180o (angle sum of )6x = 180o x = 30 A = 90o, B = 60o and ACB =30oNow, ACB + ACE + ECD = 180o (angles on a straight line) 30o + 90o + ECD = 180o

Let A, B and C be 3x, 2x and x respectively.3x +2x +x = 180o (angle sum of )6x = 180o x = 30 A = 90o, B = 60o and ACB =30oNow, ACB + ACE + ECD = 180o (angles on a straight line) 30o + 90o + ECD = 180o ECD = 180o – 120o = 60o

Let A, B and C be 3x, 2x and x respectively.3x +2x +x = 180o (angle sum of )6x = 180o x = 30 A = 90o, B = 60o and ACB =30oNow, ACB + ACE + ECD = 180o (angles on a straight line) 30o + 90o + ECD = 180o ECD = 180o – 120o = 60oHence, ECD = 60o