Answer:
A. [tex]\text{m AB}=49^o[/tex].
B. [tex]\text{m ABC}=253^o[/tex].
C. [tex]\text{m BAC}=156^0[/tex].
D. [tex]\text{m ACB}=311^o[/tex]
Step-by-step explanation:
We have been given a circle and we are asked to find the arc measures of given circle.
Since we know that the measure of an arc that subtends to central angle equals the measure of central angle.
A. We can see from our circle that arc AB subtends to central angle AOB.
[tex]m\angle AOB=49^o[/tex]
[tex]\text{m AB}=49^o[/tex]
Therefore, measure of arc AB will be also 49 degrees.
B. First of all we will have to find the measure of arc BC.
Since we know that the sum of all central angles in a circle is 360°, so we can find the measure of arc BC by subtracting measure of arcs AB and AC from 360 degrees.
[tex]\text{m BC}=360^o-(\text{m AB+m AC})[/tex]
[tex]\text{m BC}=360^o-(49^o+107^o)[/tex]
[tex]\text{m BC}=360^o-156^o[/tex]
[tex]\text{m BC}=204^o[/tex]
We can see that ABC equals arc AB plus arc BC.
[tex]\text{m ABC}=\text{m AB}+\text{m BC}[/tex]
Upon substituting measures of arc AB and BC we will get,
[tex]\text{m ABC}=49^o+204^o[/tex]
[tex]\text{m ABC}=253^o[/tex]
Therefore, measure of arc ABC is 253 degrees.
C. We can see that arc BAC equals arc BA plus arc AC.
[tex]\text{m BAC}=\text{m BA}+\text{m AC}[/tex]
Upon substituting measure of arc BA and AC we will get,
[tex]\text{m BAC}=49^o+107^0[/tex]
[tex]\text{m BAC}=156^0[/tex]
Therefore, measure of arc BAC is 156 degrees.
D. We can see that arc ACB equals arc AC plus arc CB.
[tex]\text{m ACB}=\text{m AC}+\text{m CB}[/tex]
Upon substituting measure of arc AC and CB we will get,
[tex]\text{m ACB}=107^o+204^o[/tex]
[tex]\text{m ACB}=311^o[/tex]
Therefore, the measure of arc ACB is 311 degrees.
