Determine the measurement of angle D (from the image)and justify your answer.

1 Answer

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durbanville | High School Teacher | (Level 2) Educator Emeritus

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To find angle D, begin by filling in the facts based on the given information.

In `Delta DBA /_A_(2) = 106` degrees (Given)

`therefore /_A_(1) = 180-106=74`  deg  (angles on a straight line)

From the diagram: 

`DC=CB=DE=EA`        (given : DC=CB=DE=EA)

`therefore Delta DBA` is an isosceles triangle as DB=DA

`therefore /_B=/_A_(1) = 74`

`therefore /_A=180-(74+74)= 32` deg (angles of a triangle)

There are other possible reasons but this is the easiest.

If the diagram was intended to show that DC=CB and DE = EA, (but not that DC=CB=DE=EA) this would necessitate a different approach (using similar triangles) but the diagram shows all the sides equal to each other (and that BA=2CE.)  


Therefore angle D = 32 degrees