Respuesta :
Given that the external angle formed by the two tangent is 40° and the
part of [tex]m \widehat{LMJ}[/tex] is 138°, we get that [tex]m \widehat{MJ}[/tex] = 87°.
Which property can be used to find [tex]m \widehat{MJ}[/tex] ?
Using the two tangent angle theorem, we have;
[tex]m \angle K = \mathbf{ \dfrac{1}{2} \times \left(\widehat{LMJ} - \widehat{LJ} \right)}[/tex]
m∠K = 40°
[tex]m \widehat{ML}[/tex] = 138°
[tex]m \widehat{LMJ}[/tex] = [tex]m \widehat{ML}[/tex] + [tex]m \widehat{MJ}[/tex]
[tex]m\widehat{LJ} = \mathbf{360^{\circ} - \left(m\widehat{ML} + m\widehat{MJ} \right)}[/tex]
Which gives;
[tex]m \angle K = \dfrac{1}{2} \times \left(\widehat{LMJ} - \left( 360^{\circ} - \left(m\widehat{ML} + m\widehat{MJ} \right) \right)\right)[/tex]
Therefore;
[tex]m\angle K= \dfrac{1}{2} \times \left(m \widehat{ML} + m \widehat{MJ} - \left( 360^{\circ} - \left(m\widehat{ML} + m\widehat{MJ} \right) \right)\right)[/tex]
[tex]40^{\circ}= \mathbf{ \dfrac{1}{2} \times \left(138^{\circ} + 2 \cdot m \widehat{MJ} - 232^{\circ} \right) \right)\right)}[/tex]
Which gives;
- [tex]m \widehat{MJ}[/tex] = 87°
Learn more about two angle tangent theorem here:
https://brainly.com/question/10685817
