Question 556675: Triangle ABC has an exterior angle, ∠DAB, and two remote inner angles, ∠B and ∠C. If m∠DAB = 11x + 13, m∠B = 7x - 7 and m∠C = 9x, solve for x and find m∠A, m∠B, m∠C, and m∠DAB.
I have this question in my workbook, and no matter how much I try, I can't visualize this setup, let alone solve the problem. Can anyone help, please?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Triangle ABC has an exterior angle, DAB, and two remote inner angles, B and C.
If DAB = 11x + 13, B = 7x - 7 and C = 9x, solve for x and find A, B, C, and DAB.
:
Visualize this, Draw a triangle ABC, with AC as the base, extend the horizontal line from A to a point D to form an exterior angle DAB, This a is a horizontal line therefore:
Interior angle A = 180 - (11x + 13)
Remove the brackets
A = 180 - 11x - 13
A = -11x + 167
Now we know all three interior angles, therefore
(-11+167) + (7x-7) + 9x = 180
Combine like terms
-11x = 7x + 9x + 167 - 7 = 180
5x + 160 = 180
5x = 180 - 160
5x = 20
x = 20/5
x = 4
:
Now you can find all the angles:
A: -11(4) + 167 = 123 degree
B: 7(4) - 7 = 21 degrees
C: 9(4) = 36 degrees
Note that these add up to 180 degrees
:
The also want to know angle DAB, which would be: 180 - A
180 - 123 = 57 degrees
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Did this make sense to you now? C
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