We are given : m∠GAH = 62° m∠ADB = 148°.
We need to find : m∠AFD.
m∠GAH = 62° = m<FAD : Vertical angles.
m∠ADB + m<ADF = 180° : Linear pair angles.
Substituting m∠ADB = 148°
148° + m<ADF = 180°
Subtracting 148 from both sides, we get
148°-148 + m<ADF = 180°-148
m<ADF = 32°
Now,
Sum of all angles of a triangle is =180°.
Therefore,
m<FAD + m<ADF + m∠AFD = 180°.
Substituting m<FAD = 62° and m<ADF = 32°, we get
62+32 + m∠AFD = 180°.
94 + m∠AFD = 180°
Subtracting 94 from both sides, we get
94-94 + m∠AFD = 180°-94
m∠AFD = 86°.
Therefore, m∠AFD = 86°.