1 answer:
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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