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Determine the measurement of angle D (from the image)and justify your answer.
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High School Teacher
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
Posted by durbanville on August 20, 2013 at 6:50 AM (Answer #1)
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