A summer camp counselor wants to find a length, $x$

in feet, across a lake as represented in the sketch

above. The lengths represented by $A B, E B, B D,$ and

$C D$ on the sketch were determined to be 1800 feet,

1400 feet, 700 feet, and 800 feet, respectively.

Segments $A C$ and $D E$ intersect at $B$ , and $\angle A E B$

and $\angle C D B$ have the same measure. What is the

value of $x ?$

## Discussion

## Video Transcript

Okay, so we're looking for the ratio of B C to A B, and we know that we're given these two triangles. And what we have to know is that if this is nine degrees and this is thirty two degrees, we know that the total interior angle some triangle is one eighty weaken do ninety plus thirty two plus angle B must equal one eighty. So if we subtract ninety and thirty two from both sides, we actually find out that he is fifty feet. Agrees. So that means that for these two triangles, they're basically the same triangle. Because if this is fifty eight and this must be thirty too So then we know that a and hear the same b and dear the same and see and effort to see. So I'm gonna make it easier on us by drawing lines of the same color. Okay, but then it says that we want B c over a B, which is just the blue line over the A b with just the black line. If we want that for the other triangle, then we know it's going to be the blue Line again, which is dia over the black line, which is d so that one is just gonna B c d e f or hurting yourself b

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