As we know, eyes are windows of our heart, which can change color with emotion. When you are angry, the IOP increases. Some blood capillary on the eyeballs break. So, apparently, the eyes look red because of broken capillary. It is very dangerous because some can lead to temporary blindness. In my opinion, when you get mad, try deep breath, and get rid of the mad things and emotions. Soft music and warm bath are effective way to relax your mad nerves.
When you get mad, your emotion is irritated. The nerves in your whole body will be stimulated. Your eyes may get the blood shot at the very short time. That is why you get the red eyes through the bad mood. You'd better keep calm at your mood. The bad mood will also affect your health. You should keep the smile to be healthy at both eyes and health.
Bad mood can lead to red eyes. When one is getting mad, the blood pressure of the body is rising, the heatbeat is accelerating, the blood flow is speeding up, as there are many blood capillary in the eyes, so the eyes appear red. It is a normal phenomenon, but you should control your mood, a good mood is important, after all.