194,241 views
7 votes
7 votes
Calculate the measure of angle L

Calculate the measure of angle L-example-1
User Cong Ma
by
3.0k points

1 Answer

22 votes
22 votes

Answer: 15

==================================================

Step-by-step explanation:

Lines LM and LP are tangent to the circle at points M and P respectively. The dashed radius lines are perpendicular to those tangents, which means we have 90 degree angles at points M and P.

For any quadrilateral, the four angles always add to 360 degrees.

L+M+O+P = 360

L+90+165+90 = 360

L+345 = 360

L = 360-345

L = 15

Another route you can use is the fact that opposite angles L and O are supplementary

L+O = 180

L+165 = 180

L = 180-165

L = 15

User Rahul Mane
by
3.0k points