Answer:
[tex]\huge\boxed{m\angle P = 94\textdegree}[/tex]
Step-by-step explanation:
In order to answer this question, we need to note a couple of things about the angle relationships in a pentagon.
- A) The sum of the measures in a pentagon will be 540° (We know this because the angle sum formula tells us that an n sided polygon angles will have a sum of [tex](n-2) \cdot 180[/tex] - 180 * 3 = 540).
- B) Equations can represent angle measures, added together will help us determine their value.
Since we know the sum of all of the angles will be 540, we can create an addition statement to find out the value of x.
[tex]132 + (4x-10) + (5x-11) + 128 + (4x+2)=540[/tex]
Let's solve for x.
- Combine the angles we already know:
- [tex]132 + 128 =260[/tex]
- Combine like terms:
- [tex]260 + 13x - 19=540[/tex]
- Add 19 to both sides, subtract 260 from both sides:
- [tex]13x =299[/tex]
- Divide both sides by 13:
- [tex]x = 23[/tex]
Now that we know the value of x, we can substitute it into the expression for point P ([tex]4x+2[/tex]) to find it's value.
- [tex]4 \cdot 23 + 2[/tex]
- [tex]92+ 2[/tex]
- [tex]94[/tex]
Therefore, the angle of measure P is 94°.
Hope this helped!
