the ratio of m<PQR to m<PQS is 5:9 what is m<RQS
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Let x represent the measure of angle PQR.
Since the ratio of m<PQR to m<PQS is 5:9, the measure of angle PQS can be represented as (9/5)x.
The sum of the measures of angles PQR, PQS, and RQS is 180 degrees.
Therefore, x + (9/5)x + m<RQS = 180.
Simplifying the equation, we get (14/5)x + m<RQS = 180.
If we divide both sides by 14/5, we get x + m<RQS = (180)/(14/5).
Reducing the right side of the equation, we get x + m<RQS = 900/14.
Converting the fraction to a decimal, we get x + m<RQS ≈ 64.2857.
Since m<RQS is an angle measure, we can round it to the nearest whole number.
Therefore, m<RQS ≈ 64.
None of the given answer options match the calculated result.