sandy wrote:
Attachment:
Capture.JPG
Quantity A |
Quantity B |
DC |
AB |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Since angles on a line must add to 180°, we know that ∠ABD + 2x = 180°
So, ∠ABD =
180° - 2x (see above)
Next, we'll let y = ∠ADB
Since angles in a triangle add to 180°, we can write: x + y + (
180 - 2x) = 180°
Simplify: y - x + 180 = 180
Subtract 180 from both sides: y - x = 0
So, it must be the case that y = x
Since we now know that ∆ABD has two equal angles (each measuring x°), we know that side AB = side BD
Finally, since ∆BCD has two equal angles (each measuring 2x°), we know that side BD = side DC
We now know that AB = BD and BD = DC
So, we can write: AB = BD = DC, which means AB = DC
Answer: C
Cheers,
Brent