Question

given: in circle e, • mjc = 59.1° • mjcm = 181.8° use the interactive diagram to determine mcm

Explanation:

Step1: Recall arc - addition property

The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs. That is, if $\overset{\frown}{JCM}=\overset{\frown}{JC}+\overset{\frown}{CM}$, then $\overset{\frown}{CM}=\overset{\frown}{JCM}-\overset{\frown}{JC}$.

Step2: Substitute given values

We know that $m\overset{\frown}{JC} = 59.1^{\circ}$ and $m\overset{\frown}{JCM}=181.8^{\circ}$. Substituting these values into the formula $m\overset{\frown}{CM}=m\overset{\frown}{JCM}-m\overset{\frown}{JC}$, we get $m\overset{\frown}{CM}=181.8 - 59.1$.

Step3: Calculate the result

$m\overset{\frown}{CM}=122.7^{\circ}$.

Answer:

$122.7^{\circ}$