Answer:
- LP is a ray
- m∠LMO = 90°
- m∠LPO = 90°
- m∠MLP = 26°
- arc MP = 154°
- arc MNP = 206°
Explanation:
You want various angle and arc measures in the given figure.
Relationships
The relevant angle relationships are ...
- a radius to a point of tangency makes a right angle with the tangent
- an arc has the same measure as its central angle
- the sum of the arcs of a circle is 360°
- the sum of angles in a quadrilateral is 360°
- an angle is formed from two rays whose endpoints are the vertex of the angle
These answer the given questions as follows:
LP is a ray.
The angle at M is 90°.
The angle at P is 90°.
The angle at L is 360° -90° -90° -154° = 26°
Arc MP has the same measure as angle MOP, 154°
Arc MNP completes the circle, so is 360° -154° = 206°