in an experment a laser contacts a flat decetor so that one angle between the laser beam and the detector is 57 less than two times the other angle . what is the measurement of the larger angle

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- Apr 16th 2006, 10:45 PMjim1174word problem
in an experment a laser contacts a flat decetor so that one angle between the laser beam and the detector is 57 less than two times the other angle . what is the measurement of the larger angle

- Apr 17th 2006, 12:23 AMCaptainBlackQuote:

Originally Posted by**jim1174**

add up to 180 degrees.

Let the angles be $\displaystyle \theta$ and $\displaystyle \phi$. Then we have by assumption:

$\displaystyle \theta + \phi = 180$.

Now translation the question into an equation (assume $\displaystyle \theta$ is the first angle):

$\displaystyle \theta=2 \phi-57$.

Now $\displaystyle \theta=180-\phi$, which can be substituted into the above

equation to give:

$\displaystyle

180-\phi=2\phi-57

$,

So:

$\displaystyle

3 \phi=180+57=237

$,

hence $\displaystyle \phi=79$, and $\displaystyle \theta=180-\phi=101$.

So the large angle is $\displaystyle 101^{\circ}$

RonL