The correct answer is option 1, which states that only statement 1 is true. Let`s dissect each option to understand why.

Option 1: This option states that statement 1 is true. Statement 1 mentions that the angle of the axis in relation to the plane in which the earth revolves around the sun is not constant. This statement is true because the Earth`s axis has a tilt of about 23.5 degrees, and this tilt remains constant as the Earth orbits the Sun.

Option 2: This option states that statement 2 is true. Statement 2 mentions that the amount of energy given off by the sun changes with the transparency of the atmosphere. This statement is not true because the amount of energy given off by the Sun, known as solar radiation, is not directly influenced by the transparency of the atmosphere. Instead, it is mainly influenced by the distance between the Earth and the Sun.

Option 3: This option states that both statement 1 and statement 2 are true. As explained above, statement 1 is true, but statement 2 is not true. Therefore, option 3 is incorrect.

Option 4: This option states that neither statement 1 nor statement 2 is true. This is incorrect as statement 1