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den301095 [7]
3 years ago
14

DIG DEEPER! The figure shows the angles used to make a double bank shot in an air hockey game. a. Find the value of x. b. How do

es the angle the puck hits the edge of the table relate to the angle it leaves the edge of the table? B 7 un E ETT​

Mathematics
1 answer:
Ahat [919]3 years ago
5 0

Answer:

the sides of the air hockey can be used as parallel lines.

m° = angles on a straight line add up to 180. 180 - 64 = 116. 116/2 = 58°

m = 58°

the 64° given is an alternate angle to X.

X = 64°

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Step-by-step explanation:

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Since ABCD is a parallelogram, the opposite sides will be parallel and equal,

\begin{gathered} AB=CD \\ BC=AD \end{gathered}

Consider that AC acts as a transversal to the parallel lines AB and CD, so we can write,

\begin{gathered} \angle CAD=\angle ACB\text{ (Alternate Interior Angles)} \\ BC=AD\text{ (Opposite sides of parallelogram)} \\ \angle ADB=\angle CBD\text{ (Alternate Interior Angles)} \end{gathered}

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\begin{gathered} AE=CE \\ BE=DE \end{gathered}

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