Question

Find the m<1 and m<2. Justify each answer.

Answer 1

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

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

Answer 2

`\angle 1 = 225 \°\\\angle 2 = 130\°`

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,

`50\° + \angle 1 + \angle CBA + \angle 2 = 360\°`

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

`\angle CBA + 95\° = 180\°\\\angle CBA = 180\° - 95\°\\\angle CBA = 85\°`

Replacing this angle into the first expression, we have

`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\°`

We know by given that
`AB \parallel DC`, that means BC and AD are transversals.

So, by alternate interior angles, we have

`\angle 1 = 95\°`

That means,

`\angle 1 + \angle 2 = 225\°\\95\° + \angle 2 = 225\°\\\angle 2 = 225\° - 95\°\\\angle 2 = 130\°`

Therefore,

`\angle 1 = 225 \°\\\angle 2 = 130\°`