Question

Line segment OC splits AOB into two angles. Find AOC, if AOB=155°,

and COB is 15° less than AOC.

Answer 1

m∠AOC = 85°

Explanation:

Since Line segment OC splits m∠AOB into two angles

So, we can use the following equation:

`\sf m\angle AOB =m\angle AOC + m\angle COB`

We are given that m∠AOB = 155° and m ∠COB is 15° less than AOC.

This means that we can write m ∠COB as m∠AOB - 15°. Substituting these values into the equation above, we get:

155° = m∠AOC + (m∠AOC - 15°)

Combining like terms, we get:

155° = 2AOC - 15°

Adding 15° to both sides of the equation, we get:

155° + 15° = 2AOC - 15° + 15°

170° = 2 m∠AOC

Dividing both sides of the equation by 2, we get:

`\sf (170^\circ)/(2)= ( 2 m\angle AOC)/(2)`

m∠AOC = 85°

Therefore, m∠AOC = 85°

Answer 2

m∠AOC = 85°

Explanation:

If line segment
`\sf \overline{OC}` splits ∠AOB into two angles, then:

`m\angle\textsf{AOC} + m\angle\textsf{COB} = m\angle\textsf{AOB}`

Given that ∠COB is 15° less than ∠AOC then:

`m\angle\textsf{COB} = m\angle\textsf{AOC} - 15^(\circ)`

Substitute this into the equation:

`m\angle\textsf{AOC} + m\angle\textsf{AOC} - 15^(\circ) = m\angle\textsf{AOB}`

Since m∠AOB = 155°, then:

`m\angle\textsf{AOC} + m\angle\textsf{AOC} - 15^(\circ) = 155^(\circ)`

Now, solve the equation for m∠AOC:

`\begin{aligned}m\angle\textsf{AOC} + m\angle\textsf{AOC} - 15^(\circ) &= 155^(\circ)\\\\2\cdot m\angle\textsf{AOC} - 15^(\circ) +15^(\circ)&= 155^(\circ)+15^(\circ)\\\\2\cdot m\angle\textsf{AOC}&= 170^(\circ)\\\\ m\angle\textsf{AOC}&= (170^(\circ))/(2)\\\\m\angle\textsf{AOC}&= 85^(\circ)\end{aligned}`

Therefore, the measure of angle AOC is 85°.