This is VERY helpful. Finally get it. Thanks a lot!
KHow wrote:
Could someone provide more insight about the rules related to this problem? I am having trouble correctly solving this one. Thank you!
reto wrote:
Attachment:
E89063a.png
If O is the center of the circle shown above, what is the measure of x?
A. 30°
B. 40°
C. 50°
D. 80°
E. 100°
Attachment:
inscribed angles 2019.1.17.png
KHow , sure.
One central angle and one inscribed angle intercept
the same arc, in my diagram,
arc ABCentral angle measure yields arc measure
Arc measure yields inscribed angle measure \(= x\)
A central angle is formed by two radii,
OA and
OB with its vertex at center O
• degree measure of central angle ∠ AOB
Straight line = 180°
Two angles that lie on a straight line sum to 180°
100° + ∠AOB = 180°
∠ AOB = 80°1) ∠ AOB is "subtended" by arc AB, or ∠ AOB intercepts arc AB
2) degree measure of intercepted arc AB ?
The radii of sector AOB intercept the circumference of the circle and create
arc AB.We cam also say that ∠ AOB "subtends" arc AB
Rule: The length of an arc subtended by a central angle has the same degree measure as the central angle∠ AOB = 80°
Because ∠ AOB is a central angle,
arc AB also
= 80°3) from degree measure of arc AB, find inscribed ∠ ACB measure = \(x\)
An inscribed angle is formed by two intersecting chords,
AC and
BC, whose vertex lies on the circumference of the circle
4) An inscribed angle has a degree measure that is \(\frac{1}{2}\) that of the arc it intercepts
Rule: the degree measure of an inscribed angle is half that of the arc that the angle intercepts5) arc AB = 80°
6) x =?
∠ ACB = \(x = \frac{1}{2}\) of arc AB
\(x = \frac{1}{2} * 80°\)
\(x = 40°\)
Answer B
Hope that helps.
This site, here, and
this site, here discuss the relationship between and among inscribed angles, central angles, and intercepted arcs