Is 137 87 blood pressure normal?

No, 137/87 mm Hg is not normal blood pressure.

It’s considered to be Stage 1 hypertension (high blood pressure), also called prehypertension.

According to the American Heart Association, normal blood pressure is less than 120/80 mm Hg. A blood pressure reading between 120/80 mm Hg and 129/80 mm Hg is considered to be elevated, and a reading of 130/80 mm Hg or higher is considered to be high blood pressure.