Question

Trisection in an angle finding the measures: see picture

Answer 1

<MNP : <PNQ : <QNO = 4:5:6

4 + 5 + 6 = 15

<MNO = 90° so 90°/ 15 = 6

<MNP = 4 x 6° = 24°
<PNQ = 5 x 6° = 30°
<QNO = 6 x 6° = 36°

<PNO = <PNQ + <QNO = 30° + 36° = 66°

Answer
<PNO = 66°