1. The major arc ED has measure 180 degrees since ED is a diameter of the circle. The measure of arc EF is 
, so the measure of arc DF is
The inscribed angle theorem tells us that the central angle subtended by arc DF, 
, has a measure of twice the measure of the inscribed angle DEF (which is the same angle OEF) so
so the measure of arc DF is also 64 degrees. So we have
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2. Arc FE and angle EOF have the same measure, 56 degrees. By the inscribed angle theorem,
Triangle DEF is isosceles because FD and ED have the same length, so angles EFD and DEF are congruent. Also, the sum of the interior angles of any triangle is 180 degrees. It follows that
Triangle OFE is also isosceles, so angles EFO and FEO are congruent. So we have
Answer:
X=7
Step-by-step explanation:
Can you try rewording this question?
Answer:?????????
Step-by-step explanation:
If the angle G is moved to a different spot in the circle the angle FGH and angle FEH in the cyclic quadrilateral will change to make it supplementary.
<h3>How to find angles of cyclic quadrilateral?</h3>
A cyclic quadrilateral is inscribed in a circle. It has all its vertices on the circumference of the circle.
Opposite angles in a cyclic quadrilateral are supplementary angles. That means they add up to 180 degrees.
Therefore,
∠F + ∠H = 180°
∠G + ∠E = 180°
Hence, if we moved ∠G to a different spot on the circle, angle FGH would change but angle FEH will also change to make the two opposite angles supplementary.
Therefore, Felix was wrong.
learn more on cyclic quadrilateral here: brainly.com/question/21208662
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