A quadrilateral, has 4 sides and its internal angles sum, add up to 360, now... you have 3 angles give.. .but we don't have C

so.. C is the difference of all the three angles from 360 or $\bf \measuredangle C=360-x-(2x+1)-148\implies \measuredangle C=360-x-2x-1-148$ whatever that is, now, you'll get some value in x-terms

so.... now once we know what C is

you can if you want, do a search in google for "inscribed quadrilateral conjecture", I can do a quick proof if you need one

but in short, for a quadrilateral inscribed in a circle, each pair of opposites angles are "supplementary angles", namely they add up to 180°

so.. what the dickens does all that mean? well D+B=180 and A+C = 180

now. we know what A is, 2x+1
and by now, you'd know what C is from 360-x-2x-1-148

so... add them together then and

$\bf \begin{array}{cccclllll}
A&+&C&=&180\\
\uparrow &&\uparrow \\
(2x+1)&+&(360-x-2x-1-148)&=&180
\end{array}$

solve for "x"

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3 years ago

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