Answer: 12. (174) 13. (73) 15. (6) 16. (332) 17. (107)
Step-by-step explanation:
#12 (mPQ = 174°):
We know that the sum of angles around a point is 360°.
Therefore, we have: [ m\angle N + m\angle P + m\angle Q = 360^\circ ]
Given:
(m\angle N = 118^\circ)
(m\angle P = 68^\circ)
Solving for (m\angle Q): [ m\angle Q = 360^\circ - 118^\circ - 68^\circ = 174^\circ ]
#13 (mOQ = 73°):
Since (m\angle PNO = 34^\circ), we can find (m\angle NOQ): [ m\angle NOQ = 180^\circ - m\angle PNO = 180^\circ - 34^\circ = 146^\circ ]
Now, (m\angle OQ) is half of (m\angle NOQ): [ m\angle OQ = \frac{1}{2} \cdot 146^\circ = 73^\circ ]
#15 (mNOP = 6°):
The sum of angles in triangle NOP is 180°: [ m\angle NOP = 180^\circ - m\angle N - m\angle P = 180^\circ - 118^\circ - 68^\circ = 180^\circ - 186^\circ = -6^\circ ]
Since angles cannot be negative, we take the positive value: [ m\angle NOP = 6^\circ ]
#16 (mLQMP = 332°):
The sum of angles in quadrilateral LQMP is 360°: [ m\angle LQMP = 360^\circ - m\angle NMO = 360^\circ - 28^\circ = 332^\circ ]
#17 (mOQN = 107°):
We already found (m\angle OQ = 73^\circ). Therefore: [ m\angle OQN = 180^\circ - m\angle OQ = 180^\circ - 73^\circ = 107^\circ ]
