Question

HELP GEOMETRY find x,y,z ASAP‼️​

Answer 1

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We have three problems that are basically the same, so let's try to come up with a general formula.

As you've observed in the previous problems I've helped you with, the angle cut off by a tangent and a chord is half that of the arc they cut off.  So, in the first two problems, if we let the angle we're given be $a$, we have $x = 2a$.

Then, by the straight-line angle rule (angles that together form a straight line sum to 180 degrees), $z = 180 - a$.  Applying the first rule again, $y = 2z = 360 - 2a$.

Applying these formulas, for the first question, $x = 115 \cdot 2 = 230$, $y = 180 - x = 65$, and $z = 360 - 2a = 130$.

For the second problem, $x = 180$, $z = 90$, and $y = 180$.

For the third, the variables are positioned differently, so we replace $x$ with $z$ (because $z$ is now the arc cut off by our given angle) and $z$ with $x$.

So, $z = 2 \cdot 134 = 268$, $x = 180 - 134 = 46$, and $y = 2x = 92$.

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