Answer:
[tex]\overleftrightarrow{AL} \parallel \overleftrightarrow{UK} \ \ \huge \checkmark[/tex]
[tex]m\angle MBK=90^{\circ }\ \huge \checkmark[/tex]
Step-by-step explanation:
We are given :
[tex]\overleftrightarrow{AM} \perp \overleftrightarrow{MN}[/tex]
and
[tex]\overleftrightarrow{UK} \perp \overleftrightarrow{MN}[/tex]
………………………………………………
The lines AM and UK are perpendicular to the same line MN.
Then
[tex]\overleftrightarrow{AM} \parallel \overleftrightarrow{UK}[/tex]
We also have :
[tex]\overleftrightarrow{AM} = \overleftrightarrow{AL}[/tex]
Therefore ,
[tex]\overleftrightarrow{AL} \parallel \overleftrightarrow{UK}[/tex]
………………………………………………………
∠MBK and ∠UBN are two vertically opposite angles.
Then
m∠MBK = m∠UBN
Since , m∠UBN = 90°
Then
m∠MBK = 90°
