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

Find the m<1 and m<2. Justify each answer.-example-1
User RayofHope
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2 Answers

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

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

User MokaT
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8.4k points
6 votes

Answer:


\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\°

User Spaleja
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