For the angle MPN we know that is oposite to the angle QPL so the will be equal so:
![\angle MPN=125º](https://tex.z-dn.net/?f=%5Cangle%20MPN%3D125%C2%BA)
Now with the value of MPN we can made an equation for x so:
![125=2x+10](https://tex.z-dn.net/?f=125%3D2x%2B10)
and we solve for x
![\begin{gathered} 125-10=2x \\ \frac{115}{2}=x \\ 57.5=x \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20125-10%3D2x%20%5C%5C%20%5Cfrac%7B115%7D%7B2%7D%3Dx%20%5C%5C%2057.5%3Dx%20%5Cend%7Bgathered%7D)
and the angle LPM will be the complementari angle of 125 so:
Answer:
5
Step-by-step explanation:
Angle-5 and angle-7 are 'vertical angles', so they're equal,
and we can write ...
<u>10x- 9 = 9x</u>
Subtract 9x from each side: x - 9 = 0
Add 9 to each side: <u> x = 9</u>
Now that we know what 'x' is, we can find the size of Angles-5 and -7 .
Angle-7 = 9x = 81° .
Now look at Angle-6 ... the one that's the answer to the problem.
Angle-6 and -7 together make a straight line, so they must
add up to 180°.
<u>Angle-6 + 81° = 180°</u>
Subtract 81° from each side: Angle-6 = <em>99° .</em>