# Math Help - word problem

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 $\theta$ and $\phi$. Then we have by assumption:

$\theta + \phi = 180$.

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

$\theta=2 \phi-57$.

Now $\theta=180-\phi$, which can be substituted into the above
equation to give:

$
180-\phi=2\phi-57
$
,

So:

$
3 \phi=180+57=237
$
,

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

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

RonL