- The measure of arc LP is 92°.
- The measure of angle LNP is half the measure of arc LP, so it is 46°.
- The measure of angle LMP is given as 68°.
- In triangle LMP, the sum of angles is 180°. So, angle LPM = 180° - 68° - 46° = 66°.
- Angle LPM and angle LNM are inscribed angles subtending the same arc LM, so they are equal. Therefore, angle LNM = 66°.
- In triangle LMN, the sum of angles is 180°. So, angle LMN = 180° - 68° - 66° = 46°.
- Angle LMN and angle LPN are inscribed angles subtending the same arc LN, so they are equal. Therefore, angle LPN = 46°.
- In triangle LPN, the sum of angles is 180°. So, angle PLN = 180° - 46° - 46° = 88°.
- Angle PLN and angle PMN are inscribed angles subtending the same arc PN, so they are equal. Therefore, angle PMN = 88°.
- In triangle PMN, the sum of angles is 180°. So, angle PNM = 180° - 88° - 46° = 46°.
- The central angle MON subtends arc MN. The inscribed angle MPN subtends the same arc MN. Angle MPN is part of triangle LMP and equals 66°. Therefore, angle MON = 2 * 66° = 132°.
Parent Tip: Review the logic above to help your child master the concept of inscribed and central angles worksheet.
