Answer:
Therefore m∠ OZQ = 32°.
Step-by-step explanation:
Given:
[tex]m\angle OZP =6x + 4\\m\angle QZP =3x + 10\\\\m\angle OZQ =18x - 4[/tex]
To Find:
m∠ OZQ = ?
Solution:
Angle Addition property:
The angle addition postulate states that if a point is within an angle and you add the two angles that are made by drawing a line through the point that the total will equal the large angle.
i.e In the Figure we will have
[tex]\textrm{By Angle Addition Property}\\m\angle OZP +m\angle QZP=m\angle OZQ\\ 6x + 4+3x + 10 =18x - 4\\9x+14=18x-4\\18x-9x=14+4\\\9x=18\\x=\frac{18}{9} \\x=2[/tex]
Now substituting x = 2 in angle OZQ we get,
[tex]m\angle OZQ = 18x-4\\m\angle OZQ = 18\times 2 - 4\\m\angle OZQ = 36-4=32\°\\\therefore m\angle OZQ = 32\°[/tex]
Therefore m∠ OZQ = 32°.
