Since AE and BD are both radii of the circle, they must be congruent. Therefore, triangle ADC is isosceles.
This means that m∠CAD = m∠CDA
Since AB bisects EF, it must be perpendicular to EF. Therefore, m∠AFC = 90 degrees.
Since BF is a straight line, m∠BFA must be 90 degrees as well.
This means that m∠DCF = 180 - m∠DCF - m∠CAD = 180 - (m∠CDA + m∠CAD) = 180 - 2m∠CAD
Since the sum of angles in a triangle equals 180 degrees, we have the following equation:
m∠CFD + m∠CDF + 2m∠CAD = 180
Substitute in the given information:
(7x - 4) + 180 - 2(7x - 4) = 180
7x - 4 + 180 - 14x + 8 = 180
176 - 7x = 180
176 - 180 = 7x
-4 = 7x
x = -4/7
Therefore, the value of x is -4/7.
Study the following diagram of circle C,
where AB¯¯¯¯¯¯¯¯
is a diameter that bisects the chord EF¯¯¯¯¯¯¯¯.
The circle as described in the problem. Segments C E and C F are marked congruent. If m∠ACF=2(7x−4),
what is the value of x?
Enter the correct value.
1 answer