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EleoNora [17]
3 years ago
7

*****50 POINTSSSS*****

Mathematics
1 answer:
defon3 years ago
6 0

Answer:

<h3>Given</h3>
  • m∠REG = 78°
  • mAR = 46°
  • ER ≅ GA
<h3>Solution</h3>
  • m∠GAR = 180° - m∠REG = 180° - 78° = 102° (supplementary angles sum to 180°)
  • m∠TAR = 1/2mAR = 1/2(46°) = 23°   (tangent chord angle is half the size of intercepted arc)
  • m∠GAN = 180° - (m∠TAR + m∠GAR) = 180° - (23° + 102°) = 55° (straight angle is 180°)
  • mAG = 2m∠GAN = 2(55°) = 110°
  • mRE = mAG = 110° (as ER ≅ GA)
  • mGE = 360° - (mAG + mAR + mRE) = 360° - (110° + 46° + 110°) = 94° (full circle is 360°)
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