1. ## word 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

2. Originally Posted by jim1174
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
This problem is not very well expressed, but let's assume that the two angles

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