Fire has meaning in the Bible as a sign of God's holiness and the light of His divine glory. So the light coming from the face and head of the angel of The Fear of the Lord indicates the glory of the Lord, which will shine through those believers who repent of all that is not of Christ in them. Another use of fire in Scripture is to indicate divine judgment. True wisdom is the knowledge of God's will in Christ and the sound judgment to apply it in each situation. The angel of wisdom is feminine because in Proverbs, chapters 1-9, the Hebrew noun for wisdom is feminine in gender.
Prudence always accompanies wisdom.
Prudence understands that what the believer says and does has an effect upon the quality and purity of the Lord's work through him or her. Here we see that prudence shows foresightedness. Prudence looks ahead as directed by the Holy Spirit. Discretion in Scripture is coupled with understanding, which helps the believer choose his or her words and actions so as to accomplish the results that are pleasing to God. It is choosing God's way as informed by the Holy Spirit in each circumstance.