Angle Bisectors and Calculations on a Line
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5 In the adjacent figure, $O$ is a point of the line $(xy)$, and $\widehat{yOz} = 70^{\circ}$.
$1^{\circ}$ Using a protractor, draw the bisector $[Ou)$ of the angle $\widehat{yOz}$ and the bisector $[Ov)$ of the angle $\widehat{xOz}$.
$2^{\circ}$ Calculate the angle $\widehat{uOv}$.
This question includes visual content: The image shows a geometric diagram with a horizontal line $(xy)$ and a point $O$ on it. A ray $Oz$ extends from $O$. The angle $\widehat{yOz}$ is labeled as $70^{\circ}$. There is handwritten work on the page showing the drawing of bisectors $Ou$ and $Ov$. The diagram shows calculations of $70^{\circ} / 2 = 35^{\circ}$ and $110^{\circ} / 2 = 55^{\circ}$. The resulting angle $\widehat{uOv}$ is calculated as $35^{\circ} + 55^{\circ} = 90^{\circ}$.
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Step by Step Written Solution
Let's solve this geometry problem. We are given a straight line x y with a point O on it. We also have rays Oz such that the angle y O z is seventy degrees.
Angle Bisector Geometry
First, we observe the visual representation. Ray Oz divides the upper half-plane. Since x y is a straight line, the angle x O y is one hundred eighty degrees.
We are given that angle y O z is seventy degrees. Let's add that to our diagram.
Now, we calculate angle x O z. Since they are supplementary, we subtract seventy from one hundred eighty.
The problem asks us to draw the bisectors. Ou is the bisector of angle y O z, and Ov is the bisector of angle x O z.
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