Hi there,
To solve this problem, we first need to state our givens.
Given:
Ray ZP bisects ∠OXQ so that ∠OZP = 8x - 9 and ∠PZQ = 5x + 18
Find: The value of x and the measure of each angle
Ok.. Now that we've stated all our givens and our objective, we can start solving.
Def. of an angle bisector is that it "splits" and angle into two congruent parts.
=> equate the two given expressions together.
[tex]8x-9 = 5x+18[/tex]
Steps to solve this equation:
1. Subtract 5x from both sides:
[tex]3x-9=18[/tex]
2. Add 9 to both sides:
[tex]3x=27[/tex]
3. Divide both sides by 3 to get x value
[tex]x = 9[/tex]
The value of x is 9. To find the value of the ∠OZP and ∠ PZQ, simply plug 9 back into their respective expressions. This results in ∠OZP and ∠PZQ being 63°. This means that the whole angle, ∠OZQ, measures 126 degrees. Hope this helps and have a phenomenal day!
