Respuesta :

calculista

Answer:

The measure of angle LMW is [tex]m\angle LMW=67\°[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of arc MW

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m\angle MLK=\frac{1}{2}[arc\ MW+arc\ WK][/tex]

substitute the given values

[tex]65\°=\frac{1}{2}[arc\ MW+68\°][/tex]

[tex]130\°=[arc\ MW+68\°][/tex]

[tex]arc\ MW=130\°-68\°=62\°[/tex]

step 2

Find the measure of arc LK

we know that

[tex]arc\ LM+arc\ MW+arc\ WK+arc\ LK=360\°[/tex] -----> by complete circle

substitute the given values

[tex]164\°+62\°+68\°+arc\ LK=360\°[/tex]

[tex]294\°+arc\ LK=360\°[/tex]

[tex]arc\ LK=360\°-294\°=66\°[/tex]

step 3

Find the measure of angle LMW

we know that

The inscribed angle measures half that of the arc comprising

so

[tex]m\angle LMW=\frac{1}{2}[arc\ LK+arc\ WK][/tex]

substitute the given values

[tex]m\angle LMW=\frac{1}{2}[66\°+68\°]=67\°[/tex]

Ver imagen calculista
akposevictor

Applying the inscribed angle theorem, the measure of angle LMW is found as: 67°.

What is the Inscribed Angle Theorem?

According to the inscribed angle theorem, the measure of an inscribed angle is half the measure of the arc that is intercepted.

Given:

  • m(LM) = 164°
  • m(WK) = 68°
  • m∠MLK = 65°

Find m(MK):

m(MK) = 2(m∠MLK) (inscribed angle theorem)

Substitute

m(MK) = 2(65°)

m(MK) = 130°

Find m(LK):

m(LK) = 360° - m(LM) - m(MK) (full circle)

Substitute

m(LK) = 360° - 164° - 130°

m(LK) = 66°

Therefore:

m∠LMW = 1/2[m(LK) + m(WK) (inscribed angle theorem)

Substitute

m∠LMW = 1/2[66° + 68°]

m∠LMW = 1/2[134°]

m∠LMW = 67°

Learn more about inscribed angle theorem on:

https://brainly.com/question/3538263

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