Two straight lines intersect 2x angle difference = 30 degrees. find all corners

1. At the intersection of two straight lines, angles are formed: ∠1, ∠2, ∠3, ∠4. ∠1 is more adjacent to it

∠2 by 30 °.

2. ∠1 = ∠2 + 30 °.

3. The total value of two adjacent angles, according to their properties, is 180 °:

∠1 + ∠2 = 180 °. We substitute ∠2 + 30 ° in this expression instead of ∠1:

∠2 + 30 ° + ∠2 = 180 °.

2∠2 = 150 °

∠2 = 75 °

∠1 = 75 ° + 30 = 105 °

4. ∠1 and ∠3, ∠2 and ∠4 are vertical. Therefore, according to their properties, they are equal to each other:

∠1 = ∠3 = 105 °, ∠2 = ∠4 = 75 °.

Answer: ∠1 = ∠3 = 105 °, ∠2 = ∠4 = 75 °.