From the picture below, what is the measure of GDF?

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°.

idk

step-by-step explanation: