The measure of angle ROQ is 41.5°.
We are given the following:
[tex]m<NOP = 31\\m<NOQ = 114\\[/tex]
First, find m<POQ
Thus:
[tex]m<POQ + m<NOP = m<NOQ[/tex] (angle addition postulate)
Substitute
[tex]m<POQ + 31 = 114[/tex]
[tex]m<POQ = 114 - 31\\[/tex] (subtraction property of equality)
m<POQ = 83°
Next, find m<ROQ
m<ROQ = m<POR (congruent angles)
Therefore:
2(m<ROQ) = m<POQ
2(m<ROQ) = 83°
m<ROQ = [tex]\frac{83}{2} \\[/tex]
m<ROQ = 41.5°
Learn more about angle addition postulate here:
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