Homework Help

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

user profile pic

jaysen12 | eNoter

Posted August 20, 2013 at 6:00 AM via web

dislike 1 like

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

1 Answer | Add Yours

user profile pic

durbanville | High School Teacher | (Level 1) Educator Emeritus

Posted August 20, 2013 at 6:50 AM (Answer #1)

dislike 1 like

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.)  

Ans:

Therefore angle D = 32 degrees 

Sources:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes