Answer:
m∠DFG = 48°
Step-by-step explanation:
Angles in a semicircle Theorem
The angle at the circumference in a semicircle is 90°
Therefore, if EOG is the diameter of the circle, then
m∠EDG and m∠EFG are both 90°
As the sum of the interior angles of a triangle is 180°
m∠EDG + m∠EGD + m∠DEG = 180°
⇒ 90° + 42° + m∠DEG = 180°
⇒ m∠DEG = 48°
As the angles at the circumference subtended by the same arc are equal, (i.e. angles in the same segment are equal) then
m∠DFG = m∠DEG = 48°
