Determine the following angles

1.

Part A) ∠SBE = 26°

Part B) Arc OB = 126°

2.

Part A)  ∠IDE = 55°

Part B)  Arc TD = 76°

3.  C

Step-by-step explanation:

1.

Part A)

The angle created from an arc to the opposite side of the circle is always HALF of the measure of the Arc. And if the angle subtends to the center only, that angle will be SAME measure as Arc.

∠ SBE is half of Arc SE

Arc SE is 52, so

∠ SBE = 52/2 = 26

Part B)

Arc OB is double of ∠BEO

∠BEO is 63, so

Arc OB = 63 * 2 = 126°

2.

Part A)

∠IDE subtends Arc IE

Arc IE is 110

∠IDE is half of Arc IE

so,

110/2 = 55

∠IDE = 55°

Part B)

Arc TD is double of ∠DET

∠DET is 38°

So,

Arc TD = 2 * 38 = 76°

3.

First,

∠HAT is half of Arc HT

Arc HT is given as 102, so

∠HAT = 102/2 = 51°

Now, we know 3 angles of a triangle add up to 180, thus:

67 + 51 + ∠HTA = 180

118 + ∠HTA = 180

∠HTA = 180 - 118

∠HTA = 62°

Correct answer is C