# The measurement of angle A=82 degrees(to the nearest degree). Find the measurement of angles B, C, and D to the nearest degree.(picture link below)...

The measurement of angle A=82 degrees(to the nearest degree). Find the measurement of angles B, C, and D to the nearest degree.(picture link below)

http://static.panoramio.com/photos/medium/89652115.jpg

I really don't know how to do this question. Any help will be appreciated!

durbanville | Certified Educator

To solve this problem we can use `tan theta= m` using triangles ABC and ADC.

Care that when using gradient (m) to solve angle sizes or inclination of a line, you can use this formula to find angles that are adjacent to the x-axis ONLY. So in this question we can find `/_A_(1) and /_A_(2) and /_C_(1) and /_C_(2)`   and from there we can use the properties for the angles of a triangle = 180 degrees or the exterior angle of a traingle= sum of the opposite interior angles.

So first of all we have to find the gradient-m:

`m=(y_(2) - y_(1))/(x_(2) - x_(1))`

Use the co-ordinates for line BC which will give us `/_C_(1)` `` because angle C meets the x-axis:

`m=(3-0)/(4-7)= 3/(-3)=-1`

Now apply `tantheta=m=-1` . Use the shift or second function key to find the angle size `= -45 deg` . This negative is used with 180-45 to give the external angle of 135 deg. The interior angle then `/_C(1) = 45 deg`

Now repeat with line CD which will give us `/_C_(2)`

`m=(0-(-4))/(7-4)= 4/3`

Now apply `tantheta=m=4/3`

Use the shift / second function to find the angle size `=53 deg`

therefore angle C = 53+45 = 98 degrees

Use this principle and find the angles at `A_(1) and A_(2)`  using the gradient of AB and AD(because they meet the x-axis). Then you can find B and D using the properties of a traingle mentioned above (=180 deg).

I have not solved them for you as eNotes rules allow a question and a closely related question (eg. how to use the same rules) and NOT multiple questions.

Ans. Angle C = 98 degrees.