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galina1969 [7]
2 years ago
5

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 $\angle ABQ$.

Mathematics
1 answer:
tester [92]2 years ago
7 0

Answer:

1:4

Step-by-step explanation:

If BP and BQ trisect angle ABC, then

m\angle ABP=m\angle PBQ=m\angle QBC

If BM bisects the angle MBQ, then

m\angle PBM=m\angle MBQ=x^{\circ}

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

m\angle PBQ=2m\angle MBQ=2x^{\circ}

Now,

m\angle ABQ=m\angle ABP+m\angle PBQ=2m\angle PBQ=2\cdot 2x^{\circ}=4x^{\circ}

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

\dfrac{x^{\circ}}{4x^{\circ}}=\dfrac{1}{4}

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