In the diagram, $bp$ and $bq$ trisect $\angle abc$. $bm$ bisects $\angle pbq$. find the ratio of the measure of $\angle mbq$ to the measure of $\angle abq$.

1:4

Step-by-step explanation:

If BP and BQ trisect angle ABC, then

If BM bisects the angle MBQ, then

Now, find the measure of angle ABQ in terms of x. First, note that

Now,

So, the ratio of the measure of angle MBQ to the measure of angle ABQ is

1:4

Step-by-step explanation:

Hope this helped! :)