Carcass wrote:
Attachment:
triangle.jpg
Quantity A |
Quantity B |
a + d – c – 90 |
90 – e – b – f |
Given:
Quantity A: a + d – c – 90
Quantity B: 90 – e – b – f
First recognize that, since AC||FD, ∠b = ∠c
So, we can replace b with c to get:
Quantity A: a + d – c – 90
Quantity B: 90 – e – c – f
Add c to both quantities to get:
Quantity A: a + d – 90
Quantity B: 90 – e – f
Now add 90 to both quantities to get:
Quantity A: a + d
Quantity B: 180 – e – f
Now add e and f to both quantities to get:
Quantity A: a + d + e + f
Quantity B: 180
Finally, notice that, since AC||FD, ∠d = ∠BCD
So, replace ∠d with ∠BCD to get:
Quantity A: a + ∠BCD + e + f
Quantity B: 180
At this point, we should recognize that Quantity A represents the sum of all three angles of ∆ACE
As such, Quantity A MUST equal 180
Answer: C
Cheers,
Brent
One doubt: how do we know AC is parallel to FD? The question stem does not provide this info and even the angles do not mention the same degree in the figure given.