Respuesta :

m <  1 = 95 degrees ( alternate angles theorem of parallel lines)

m < 2 = 180 - 50 = 130 degrees ( internal angles theorem of parallel lines).

Answer:

[tex]\angle 1 = 225 \°\\\angle 2 = 130\°[/tex]

Step-by-step explanation:

In this problem we have to find the measure of angle 1 and angle 2.

So, we know by definition that all internal angles of a parallelogram must sum 360°. That is,

[tex]50\° + \angle 1 + \angle CBA + \angle 2 = 360\°[/tex]

However, by sum of angles, and by supplementary angles, we have

[tex]\angle CBA + 95\° = 180\°\\\angle CBA = 180\° - 95\°\\\angle CBA = 85\°[/tex]

Replacing this angle into the first expression, we have

[tex]50\° + \angle 1 + \angle CBA + \angle 2 = 360\°\\50\° + \angle 1 + 85\° + \angle 2 = 360\°\\\angle 1 + \angle 2 = 360\° - 85\° - 50\°\\\angle 1 + \angle 2 = 225\°[/tex]

We know by given that [tex]AB \parallel DC[/tex], that means BC and AD are transversals.

So, by alternate interior angles, we have

[tex]\angle 1 = 95\°[/tex]

That means,

[tex]\angle 1 + \angle 2 = 225\°\\95\° + \angle 2 = 225\°\\\angle 2 = 225\° - 95\°\\\angle 2 = 130\°[/tex]

Therefore,

[tex]\angle 1 = 225 \°\\\angle 2 = 130\°[/tex]

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