Question

Only higher experienced need answer theorems all 5 questions. Thank you 200points if repeating the last question.

Answer 1

15° created a 230 ° arc

360 - 230 = 130°

that means ∠EDG = 1/2 (130) or 65°

second : ∠ABD = 180 - 112 = 68

The arc created APD is 2 times ∠ABD or 136°, therefore ∠x = 136°.

Central Angles and arcs are equal

360° - 136° = 224°

224° is the arc created by ∠APD. Take 1/2 of 224° and you get 112°

Third: ∠ACB and ∠ AOB create the same arc.

since ∠ACB is 48°, the arc is 96° (twice the angle)

if the arc is 98° then the central angle ∠AOB = 98°

360°-98° = 262°

You need this because ∠APB is 1/2(262-98) or 82°

Fourth : Both inscribed angles create the same arc

so the angles are equal

∠DEG = 38°

Explanation:

Answer 2

first one : inscribed angles create arc twice their degree

so, 115° created a 230 ° arc

360 - 230 = 130°

that means ∠EDG = 1/2 (130) or 65°

second : ∠ABD = 180 - 112 = 68

The arc created APD is 2 times ∠ABD or 136°, therefore ∠x = 136°.

Central Angles and arcs are equal

360° - 136° = 224°

224° is the arc created by ∠APD. Take 1/2 of 224° and you get 112°

Third: ∠ACB and ∠ AOB create the same arc.

since ∠ACB is 48°, the arc is 96° (twice the angle)

if the arc is 98° then the central angle ∠AOB = 98°

360°-98° = 262°

You need this because ∠APB is 1/2(262-98) or 82°

Fourth : Both inscribed angles create the same arc

so the angles are equal

∠DEG = 38°