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 anglesOriginally 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