The moon and the sun have approximately the same angular size in the sky. However, it is necessary to note that their angular dimensions are equal because the orbit of the moon around the earth has the shape of an ellipse.
At the peak (402,927 km), the Moon has an angular size of 29′40 ″, and at the perigee (354,027) – 33′45 ″. The difference is almost 14%. The angular size of the Sun is on average 31′59 ″. It also varies due to the ellipticity of the Earth’s orbit, but to a much lesser extent. Therefore, talking about perfect coincidence is not necessary, only about approximate.
It is enough to look at high-quality photographs of total solar eclipses to make sure that the perfect coincidence is not really so ideal at all.
But, of course, it should be recognized that the average values of the angular dimensions of the Moon and the Sun are really close (the difference is 0′54 ″).
Why is that?
The fact is that the ratio of the distance from the Earth to the Moon to the diameter of the Moon is approximately equal to the ratio of the distance from the Earth to the Sun to the diameter of the Sun.
Could this happen by chance?
Of course. Besides, there is no doubt that what we are observing is pure coincidence if only we know for sure that in the past, the Moon was much closer to the Earth: about 10-15 times closer than now, at a distance of only 25-40 thousand kilometers. We also know that the Moon is gradually moving away from the Earth, and the Sun, on the contrary, is increasing in size.
Moreover, we not only know what it was, but we also understand the physics of the processes that led to the separation of the moon from the earth, and to the gradual increase in the size of the sun. There are no riddles or oddities in this.
We can say that we are at the right time and in the right place to observe such an approximate coincidence of the visible sizes of the heavenly bodies. In the past, the Moon had a much larger angular size than the Sun, and in the future, it will have a much smaller angular size.
To argue that such a coincidence is explained by divine providence, you just need to throw all the physics, geology, chemistry and a dozen sciences in the trash. This is about the same as arguing that paleontologists find dinosaur fossils not because dinosaurs once lived on Earth, but because someone deliberately buried dinosaur bones to confuse evolutionists.
It should also be added that it is possible that in the case of Moon, there is a selection error. It is widely believed among some scientists that the presence of a large satellite (which can also cause eclipses) is an important factor that makes life on the planet possible.
So, for example, the Moon has a stabilizing effect on the rotation of the Earth and, as a consequence, on the climate. If our planet did not have such a moon, then perhaps this question would not exist and more precisely, there would be no life on earth at all.