Answer: 70°
Step-by-step explanation:
When a tangent and a secant, two secants, or two tangents intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.
It means that, considering ML and PL as tangent lines, the measure of the angle L (m∠L) is half of the difference of the measures of the arcs MP and PM.
The measure of the first arc is m MP = 110°. There is another arc called PM, which is the arc starting on P until M, passing through N. As measure of the whole circle is 360°, mPM = 360° - 110° = 250°.
Then,
m∠L = 1/2 × | mPM - mMP |
m∠L = 1/2 × | 250° - 110° |
m∠L = 1/2 × 140°
m∠L = 140°/2
m∠L = 70°
