Angle Bisectors and Calculations on a Straight 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: A geometric diagram showing a straight horizontal line segment labeled with 'x' on the left and 'y' on the right. A point 'O' is located on this line. A ray extends from point 'O' upwards and slightly to the right, labeled with 'z' at its endpoint. The angle between the ray Oz and the segment Oy is labeled as $70^\circ$. The line segment xy is colored light blue, while the ray Oz is colored reddish-pink.
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Step by Step Written Solution
In this geometry problem, we are given a line x y with a point O on it. We also have a ray O z such that the angle y O z is 70 degrees. Our goal is to calculate the angle between the bisectors of the two adjacent angles formed.
Angle Geometry
Let's start by reconstructing the diagram. We have a horizontal line segment from x to y, with origin O in the center. Ray O z makes a 70 degree angle with O y.
Since x, O, and y lie on a straight line, the angle x O y is 180 degrees. This means the angles x O z and y O z are supplementary.
We are given that angle y O z is 70 degrees, so we can solve for angle x O z.
Subtracting 70 from 180, we find that angle x O z is 110 degrees.
Now, let's draw the bisector O u of the angle y O z. A bisector divides an angle into two equal parts.
Substituting 70 degrees for angle y O z, we get 35 degrees.
Next, we draw the bisector O v of the angle x O z. Similarly, this divides the 110 degree angle into two equal parts.
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