Bunuel wrote:

What is a + b + c + d?

A. 110

B. 120

C. 130

D. 150

E. Cannot be determined from the information above

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The attachment **Multipoint_ABCD.png** is no longer available

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

Attachments

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