How do you do this question?

Mathematics

2 answers:

beks73 [17]3 years ago

8 0

The length of a circular arc (s) is the product of the circle's radius and the central angle measure in radians.

... s = r·θ

Then the central angle measure in radians is ...

... θ = s/r

For your problem, you have s = 8π/9 and r = 1. Then the central angle AOC is

... ∠AOC = (8π/9)/(1) = 8π/9 . . . . radians

The relationship between radians and degrees is

... 180° = π radians

Multiplying this equation by 8/9 will tell us the degree measure of ∠AOC.

... 8/9×180° = (8/9)×π radians

... ∠AOC = (8/9)·180° = 160°

We know that this is the sum of the two (equal) central angles ∠AOB and ∠BOC, so we have

... 2×∠AOB = 160°

... ∠AOB = 160°/2 = 80°

_____

Here, you know that 8π/9 is the central angle <em>in radians</em> because the ratio of arc length to radius is the angle <em>in radians</em>.

Hitman42 [59]3 years ago

4 0

The central angle corresponding to AOB is half of the 8pi/9 radians mentioned, meaning that the central angle of AOB is 4pi/9.

Converting that to degrees:

4pi/9 180 degrees

-------- * -------------------- = 80 degrees.

1 pi

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ololo11 [35]

Answer:

From the graph attached, we know that $\angle 1 \cong \angle 5$ by the corresponding angle theorem, this theorem is about all angles that derive form the intersection of one transversal line with a pair of parallels. Specifically, corresponding angles are those which are placed at the same side of the transversal, one interior to parallels, one exterior to parallels, like $\angle 1$ and $\angle 5$ .

We also know that, by definition of linear pair postulate, $\angle 3$ and $\angle 1$ are linear pair. Linear pair postulate is a math concept that defines two angles that are adjacent and for a straight angle, which is equal to 180°.

They are supplementary by the definition of supplementary angles. This definition states that angles which sum 180° are supplementary, and we found that $\angle 3$ and $\angle 1$ together are 180°, because they are on a straight angle. That is, $m \angle 3 + m \angle 1 = 180\°$

If we substitute $\angle 5$ for $\angle 1$ , we have $m \angle 3 + m \angle 5 = 180\°$ , which means that $\angle 3$ and $\angle 5$ are also supplementary by definition.