The measure of arc GDF is 304°
Solution:
Given data:
m∠CHD = 90°, m(ar EF) = 34°
The angle measure of the central angle is equal to the measure of the intercepted arc.
m∠CHD = m(ar CD) = 90°
Sum of the adjacent angles in a straight line = 180°
⇒ m∠GHC + m∠CHD = 180°
⇒ m∠GHC + 90° = 180°
Subtract 90° from both sides, we get
⇒ m∠GHC = 90°
⇒ m(ar GC) = m∠GHC
⇒ m(ar GC) = 90°
Sum of the adjacent angles in a straight line = 180°
⇒ m∠EHD + m∠CHD = 180°
⇒ m∠EHD + 90° = 180°
Subtract 90° from both sides, we get
⇒ m∠EHD = 90°
⇒ m(ar ED) = m∠EHD
⇒ m(ar ED) = 90°
m(ar GDF) = m(ar GC) + m(ar CD) + m(ar DE) + m( EF)
= 90° + 90° + 90° + 34°
= 304°
The measure of arc GDF is 304°.