Bunuel wrote:
What is a + b + c + d?
A. 110
B. 120
C. 130
D. 150
E. Cannot be determined from the information above
Attachment:
Multipoint_ABCD.png
Nice question!!
I can see some triangles that include the necessary angles (a, b, c and d)
So, let's add some extra angles, x and y:
Since x, 30 and y are on a line, we know that
x + y + 30 = 180
This means that
x + y = 150Now let's examine some hidden triangles. Here's one:
Since angles in a triangle add to 180 degrees, we can write: a + c + x + 30 = 180
Subtract 30 from both sides to get:
a + c + x = 150Here's another hidden triangle
Since angles in a triangle add to 180 degrees, we can write: b + d + y + 30 = 180
Subtract 30 from both sides to get:
b + s + y = 150We now have two equations:
a + c + x = 150b + s + y = 150ADD them to get: a + b + c + d + x + y = 300
Since
x + y = 150, we can write: a + b + c + d +
150 = 300
Subtract 150 from both sides to get: a + b + c + d = 150
Answer:
Cheers,
Brent
Sorry for using your image.
I am using it to arrive at answer using different approach.
I will try to explain using Theorem: An exterior angle of a triangle is equal to the sum of the opposite interior angles.
and x+y+30 =180.
Putting x and y value in above equation.
Good, good Let the kudos flow through you