What is the measure of angle KPM?

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The measure of angle KPM can be determined using the equation derived from the bisector theorem. Given that ray PK bisects angle LPM, where the measure of angle LPM is 11x degrees and angle LPK is (4x + 18) degrees, the correct equation is 2(4x + 18) = 11x. Solving this yields x = 12, leading to the conclusion that angle LPK measures 66 degrees, confirming option e as the correct answer.

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karush
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ray $\overline{PK}$ bisects the meausre of
$\angle{LPM}$ is $11x^o$ and the measure of $\angle{LPK}$ is $(4x+18)^o$
What is the measure of $\angle{KPM}$

a. $12^o\quad$ b, $28\dfrac{2}{7}^o\quad$ c. $42^o\quad$ d. $61\dfrac{1}{5}^o\quad$ e. $66^o$

ok I think this could be done by observation but that can be a little deceptive
so my eq to solve it was
$2(4x^o+18)=11x^o$
hopefully:unsure:

edit correct the eq
 
Last edited:
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karush said:
$2(4x^o+36)=11x^o$
Surely you mean 2(4x + 18) = 11x...

-Dan
 
$2(4x+18)=11x$
$8x+36=11x$
$36=3x$
$12=x$

$\angle{LPK}$ is $(4(12)+18)^o=(48+18)^o=66^o$ which is e
 
Last edited:
the little “o” that looks like an exponent is just the degree symbol
 
skeeter said:
the little “o” that looks like an exponent is just the degree symbol
it might be easier to drop the degree sign when taking steps
but what does x equal?
 
the steps to solve this was on the internet but everyone wanted a cc before they would show it.

I really appreciate the help I get here at MHB
 

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