Angle 3 and angle 4 are adjacent, and angle 3 is 30 ° less than angle 4. Find angle 3 and angle 4.

By definition of adjacent angles, the sum of angles 3 and 4 is 180 °.

∠3 + ∠4 = 180. (1)

∠3 + 30 = ∠4. (2)

Let us subtract from equation (1) equation (2).

∠3 + ∠4 – ∠3 – 30 = 180 – ∠4.

∠4 – 30 = 180 – ∠4.

∠4 + ∠4 = 180 + 30.

2 * ∠4 = 210.

∠4 = 105 °.

From equation (1) we express ∠3:

∠3 = 180 – ∠4.

∠3 = 180 – 105 = 75.

Answer: ∠3 = 75 °, ∠4 = 105 °.