Determine and state the measure of angle F

Mathematics

2 answers:

mezya [45]3 years ago

4 0

Answer:

∠ F = 94°

Step-by-step explanation:

The opposite angles of the quadrilateral are supplementary, thus

∠ D + ∠ F = 180°, that is

86° + ∠ F = 180° ( subtract 86° from both sides )

∠ F = 94°

Keith_Richards [23]3 years ago

3 0

Answer:

Step-by-step explanation:

Angle <D is an inscribed angle and the measure of it is equal to the half of the arc it sees

so the measure of arc EFG is 2×86° = 172°

Since the perimeter of a circle is 360° the measure of arc EDG would be 360 - 172 = 188

Therefore since the measure of angle <F should be half of the arc it sees as well the answer is 188 ÷ 2 = 94

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So, the x-cooardinate of the center is the average of the x-coordinates of P and Q:

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$C=(C_x,C_y)$

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Divide this length by 2 and you'll get the radius.

C: At this point, we have both the radius and the coordinates of the center. The equation of the circle depends on these two parameters, and it is

$(x-C_x)^2+(y-C_y)^2=r^2$

Substitute $C_x$ and $C_y$ with the coordinates of the center (found in point A.) and $r$ with the radius (found in point B.) and you'll have the equation of the circle.