2 years ago

50 POINTSSSS

Mathematics

1 answer:

defon2 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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