Question

Major arc BLJ measures 249 degrees. Find the measure in degrees of

angle K.
2490
B
J
L
K?
K

Answer 1

m∠K = 69°

Explanation:

"When two tangents or secants intersect outside the circle, exterior angle formed between the tangents of secants is one half the difference of major and minor arcs"

By this theorem,

m(∠K) =
`(1)/(2)[m(\widehat{LBJ}-m(\widehat{LJ})]`

Here,
`m(\widehat{LBJ})` = 249°

`m(\widehat{LJ})` = 360° - 249°

= 111°

m∠K =
`(1)/(2)(249-111)`

=
`(138)/(2)`

= 69°

Therefore, measure of angle K = 69° will be the answer.