Question

Circle A is intersected by LM←→ and MO←→−.

What is the measure of ∠LMO?

Enter your answer as a decimal in the box.

Answer 1

47.5 Formula is: 1/2 (angle LO- angle LN)

Answer 2

`{\angle}LMO=47.5^(\circ)`

Explanation:

We know that the circumscribed angle is the half of the difference of the major arc and the minor arc, that is

`CA=(1)/(2)(major arc- minor arc)`

Substituting the values from the figure given, we get

`{\angle}LMO=(1)/(2)(arcLO-arcLN)`

`{\angle}LMO=(1)/(2)(155^(\circ)-60^(\circ))`

`{\angle}LMO=(1)/(2)(95^(\circ))`

`{\angle}LMO=47.5^(\circ)`

Thus, the measure of
`{\angle}LMO` is
`47.5^(\circ)`.