What fraction represents the shaded part of the fraction
bar?

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Ответ:

brobles9118

12.05.2022

Mathematics

139°

Step-by-step explanation:

If EC bisects BED, then

$m\angle BEC=m\angle CED=4x+1$

By Angle Addition Postulate,

$m\angle AEB+m\angle BEC+m\angle CED=m\angle AED$

Angle AED is a straight angle with measure 180°.

$m\angle AEB=11x-12\\ \\m\angle BEC=m\angle CED=4x+1\\ \\m\angle AED=180^{\circ}$

By substitution property,

$11x-12+4x+1+4x+1=180\\ \\19x-10=180\\ \\19x=190\\ \\x=10$

By Angle Addition Postulate,

$m\angle AEC=m\angle AEB+m\angle BEC$

$m\angle AEB=11x-12=11\cdot 10-12=110-12=98^{\circ}\\ \\m\angle BEC=4x+1=4\cdot 10+1=41^{\circ}$

By substitution property,

$m\angle AEC=98^{\circ}+41^{\circ}=139^{\circ}$

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What fraction represents the shaded part of the fraction bar?