okay since ooposite angles are supplementary in inscribed polygons than angle W is 80 degrees and angle Z is 70 degrees...right... okay now the question askes to find all angles and the measures of arc WZ and arc WX. i thought about making tow triangles cutting the 70 degress in half and multiplying by 2 to get the arc measure of WX....;/ i know i'm wrong please help and explain !
2007-06-02 07:13:33 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
http://i22.photobucket.com/albums/b346/perlasedano/Picture788.jpg
2007-06-02 07:15:14 · update #1
Opposite angles are supplementary in inscribed quadrilaterals, not in all polygons :)
The other two angles are the supplements of W and Z, namely 100* and 110*.
For the rest of the problem you need more information! Specifying the angels in an inscribed quad is not enough. For instance, all rectangles are inscribed quad's with right angles, but you can have many different rectangles inscribed in the same circle.
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Ah, your picture reveals something you didn't tell: WZ and ZY are congruent. That means that also the arcs WZ and ZY are congruent, i.e. have the same measure.
Since the measure of arc WZY is twice as larges as angle X, namely 2x110* = 220*, you can conclude that both arc WZ and arc WY have measure 110*.
As for arc WX, because the measure of arc XWZ is 2x100* = 200*, and you already know that arc WZ = 110*, you are left with 200* - 110* = 90* for arc WX.
2007-06-02 07:29:05 · answer #1 · answered by dutch_prof 4 · 1⤊ 0⤋
Draw WY forming isosceles triangle WYZ.
angle WYZ = (180-70)/2 =55 degrees.
Therefore arc WZ = 2 *55 = 110 degrees.
Angle WYX = 100 - 55 = 45degrees.
Therefore arc WX = 2*45 = 90 degrees
2007-06-02 14:36:54 · answer #2 · answered by ironduke8159 7 · 1⤊ 0⤋
the measurements of an arc = the angle/360 X 3.14
2007-06-02 14:29:54 · answer #3 · answered by Anonymous · 0⤊ 1⤋