GreenlightTestPrep wrote:
AD = BC
∠ABC = 90°
Quantity A |
Quantity B |
x |
30 |
A) The quantity in Column A is greater.
B) The quantity in Column B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Important: Even though we aren't provided any angles, we can still label many of the angles in the diagram. Since angles on a line must add to 180°, ∠ADB =
(180 - 2x)°Since angles in ∆ADB must add to 180°, ∠BAD =
x°Since ∆ADB has two equal angles (of
x°), the triangle is an isosceles triangle which means
side BD = side AD Since side BD = side BC, we have an isosceles triangle which means ∠DCB =
2x°, and since all angles must add to 180 degrees, we can see that ∠DBC =
(180 - 4x)°Finally, since ∠ABC = 90°, we can write:
x +
(180 - 4x)° = 90°
Simplify: 180 - 3x = 90
Solve:
x = 30We get:
QUANTITY A: 30
QUANTITY B: 30
Answer: C
Cheers,
Brent