Answer :
Answer:
[tex]\angle{KPM}=66[/tex]
Step-by-step explanation:
given that:
∠LPM = 11x°
∠LPK = (4x + 18)°
PK bisects ∠LPM,
we know that bisection means to divide an angle in two equal parts.
so when PK bisects ∠LPM, the remaining angles are 11x/2. hence the remaining angles are:
[tex]\angle{LPK}=\dfrac{11x}{2}\\ \angle{KPM}=\dfrac{11x}{2}[/tex]
but we have another representation of ∠LPK and that is:
[tex]\angle{LPK}=4x+18[/tex]
so both of these are equal, and can be written as:
[tex]\angle{LPK}=\angle{LPK}[/tex]
[tex]4x+18=\dfrac{11x}{2}[/tex]
we can solve for the value of x
[tex]11x-8x=36[/tex]
[tex]x=12[/tex]
Now we can find all the angles!
[tex]\angle{LPM} = 11x = 11(12) = 132[/tex]
[tex]\angle{LPK} = 4x+18 = 4(12)+18 = 66[/tex]
we can also confirm our bisection
[tex]\angle{LPK} = \dfrac{11x}{2} = \dfrac{11(12)}{2} = 66[/tex]
and since in bisection the two halves are equal
[tex]\angle{LPK}=\angle{KPM}=\dfrac{11x}{2}[/tex]
[tex]\angle{KPM}=66[/tex]