Question

which statements are correct? check all that apply. arc gf is a major arc. one major arc is (widehat{gch}). arc fe is a minor arc. the measure of (widehat{fe}) is (41^{circ}). the measure of (widehat{cg}) is equal to the measure of (angle gde). arc ghe is a semi - circle.

Explanation:

Step1: Recall arc - type definitions

A minor arc has a measure less than 180°. A major arc has a measure greater than 180°. A semicircle has a measure of 180°. The measure of an arc is equal to the measure of its central angle.

Step2: Analyze arc GF

Arc GF is a minor arc since the central - angle ∠GDF=126° + 41°=167°<180°, so "Arc GF is a major arc" is incorrect.

Step3: Analyze arc GHE

Arc GHE is a semicircle as it subtends a central angle of 180° (since the whole circle's central - angle is 360° and the non - GHE part has non - zero central angles). So "One major arc is \(\widehat{GHE}\)" is incorrect and "Arc GHE is a semicircle" is correct.

Step4: Analyze arc FE

Arc FE is a minor arc because the central angle ∠FDE = 41°<180°, so "Arc FE is a minor arc" is correct.

Step5: Analyze the measure of arc FE

The measure of arc FE is 41° since the measure of an arc is equal to the measure of its central angle ∠FDE, so "The measure of \(\widehat{FE}\) is 41°" is correct.

Step6: Analyze the measure of arc GE

The measure of arc GE is equal to the measure of ∠GDE. The measure of an arc is equal to the measure of its central angle, so "The measure of \(\widehat{GE}\) is equal to the measure of ∠GDE" is correct.

Answer:

Arc FE is a minor arc.
The measure of \(\widehat{FE}\) is 41°.
The measure of \(\widehat{GE}\) is equal to the measure of ∠GDE.
Arc GHE is a semicircle.