Question

Need help with this math problem

Answer 1

Therefore m∠ OZQ = 32°.

Explanation:

Given:

`m\angle OZP =6x + 4\\m\angle QZP =3x + 10\\\\m\angle OZQ =18x - 4`

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

`\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=(18)/(9) \\x=2`

Now substituting x = 2 in angle OZQ we get,

`m\angle OZQ = 18x-4\\m\angle OZQ = 18* 2 - 4\\m\angle OZQ = 36-4=32\°\\\therefore m\angle OZQ = 32\°`

Therefore m∠ OZQ = 32°.