Question

Please help I don't understand how to solve this, if you can please show work, thank you

Answer 1

First, use triangle angle sum theorem on the triangle on the right.

180-(43+57)=80

Use vertical angles theorem, 
the missing angle of the triangle on left is 80 as well.

Use triangle angle sum theory again.

2x+80=180,
x=50 

Answer 2

Answer:

x = 50

Step-by-step explanation:

We know:

The sum of the measures of the angles of the triangle is equal to 180°.

Therefore we have the equation:

m∠1 + 57° + 43° = 180°

m∠1 + 100° = 180°         subtract 100° from both sides

m∠1 = 80°

The angles ∠1 and ∠2 are the vertex angles, therefore they are congruent.

m∠2 = 80°.

Second equation:

x° + x° + 80° = 180°           subtract 80° from both sides

2x° = 100°       divide both sides by 2

x° = 50°