Question

if angles AOC, COB, BOD together make up 274° find each of the four angles at O.

Answer 1

Angle AOD = 360-274 = 86°
So, COB = 86° [Vertically opposite angles]
Angle AOC =180-86 = 94° [ linear pair ]
And BOD = AOC = 94° [ Vertically opposite angles]


Hope it helps....

Answer 2

Answer:

$\angle AOD = 86^{\circ}$

$\angle COB=86^{\circ}$

$\angle AOC =94^{\circ}$

$\angle BOD =94^{\circ}$

Step-by-step explanation:

$\angle AOC+\angle COB+\angle BOD+\angle AOD =360^{\circ}$ --1

We are given that $\angle AOC+\angle COB+\angle BOD=274^{\circ}$

Substitute the value in 1

$274^{\circ}+\angle AOD =360^{\circ}$

$\angle AOD =360^{\circ}-274^{\circ}$

$\angle AOD =86^{\circ}$

Now $\angle AOD=\angle COB$  (vertical angles)

So, $\angle AOD= \angle COB=86^{\circ}$

Now $\angle AOC+\angle COB =180^{\circ}$  (Linear Pair)

$\angle AOC+86^{\circ} =180^{\circ}$

$\angle AOC =180^{\circ}-86^{\circ}$

$\angle AOC =94^{\circ}$

$\angle AOC=\angle BOD$  (vertical angles)

So, $\angle AOC=\angle BOD =94^{\circ}$

Hence  $\angle AOD = 86^{\circ}$

$\angle COB=86^{\circ}$

$\angle AOC =94^{\circ}$

$\angle BOD =94^{\circ}$