Question

Please help me with the following questions. You don’t have to add long explanations, just very short ones.

Thanks.

Answer 1

1) a° = 68°

2) a° = 34°

3) a° = 180°

4) arc AB = 84°

5) m∠AOB = 120°

6) a° = 124°, b° = 62°

Explanation:

Question 1

According to the Inscribed Angle Theorem, the measure of an inscribed angle in a circle is equal to half the measure of the intercepted arc. Therefore:

`\rm a^(\circ)=(1)/(2) \cdot 136^(\circ)`

`\rm a^(\circ)=68^(\circ)`

`\hrulefill`

Question 2

According to the Inscribed Angle Theorem, the measure of the intercepted arc is twice the measure of the inscribed angle. Therefore:

`\rm a^(\circ)=2\cdot 17^(\circ)`

`\rm a^(\circ)=34^(\circ)`

`\hrulefill`

Question 3

According to the Inscribed Angle Theorem, the measure of the intercepted arc is twice the measure of the inscribed angle. Therefore:

`\rm a^(\circ)=2\cdot 90^(\circ)`

`\rm a^(\circ)=180^(\circ)`

`\hrulefill`

Question 4

The measure of the central angle of a circle is equal to the measure of the corresponding intercepted arc. Therefore:

`m\overset{\frown}{\rm AB}=84^(\circ)`

`\hrulefill`

Question 5

The measure of the central angle of a circle is equal to the measure of the corresponding intercepted arc. Therefore:

`m \angle\rm AOB=120^(\circ)`

`\hrulefill`

Question 6

The sum of the central angles (or the corresponding intercepted arcs) in a complete circle always adds up to 360°. Therefore:

`\rm a^(\circ)+136^(\circ)+100^(\circ)=360^(\circ)`

Solve for a:

`\rm a^(\circ)+236^(\circ)=360^(\circ)`

`\rm a^(\circ)=124^(\circ)`

According to the Inscribed Angle Theorem, the measure of an inscribed angle in a circle is equal to half the measure of the intercepted arc. Therefore:

`\rm b^(\circ)=(1)/(2) \cdot a^(\circ)`

`\rm b^(\circ)=(1)/(2) \cdot 124^(\circ)`

`\rm b^(\circ)=62^(\circ)`