Anyone teach me the angles in theorms

Question

asked Dec 10, 2020 152k views

1 Answer

Alexander Jank · Answer 1 · 2020-12-16T14:27:02+0000

The alternate segment theorem says that angles BAC and BCE are congruent, so

$m\angle BAC=24^\circ$

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Triangle ABC is isosceles, which makes angles ACB and ABC congruent, and the sum of the interior angles of any triangle is 180 degrees, so

$m\angle ACB+m\angle ABC+m\angle BAC=180^\circ$

$2m\angle ABC+24^\circ=180^\circ$

$m\angle ABC=78^\circ$

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The alternate segment theorem also says that angles DCF and CAD are congruent. Angles DCF, ACD, ACB, and BCE are supplementary, so

$m\angle DCF+m\angle ACD+m\angle ACB+m\angle BCE=180^\circ$

$m\angle DCF=m\angle CAD=49^\circ$

Then

$m\angle ADC+m\angle ACD+m\angle CAD=180^\circ$

$m\angle ADC=102^\circ$

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The inscribed angle theorem says that angle COB has twice the measure of angle BAC, so

$m\angle COB=48^\circ$