OC bisects AOB, OD bisects AOC, OE bisects AOD, OF bisects AOE, OG bisects BOF. if BOF =120°, find DOE
1 answer:
Answer:
∠DOE = 16°
Step-by-step explanation:
The given parameters are;
∠BOF = 120°
∠AOB = 2×∠AOC Given
∠AOC = 2×∠AOD Given
∠AOD = 2×∠AOE Given
∠AOE = 2×∠AOF Given
Therefore;
∠AOB = 16×∠AOF Angle addition postulate
∠BOF = ∠AOB - ∠AOF = 16×∠AOF - ∠AOF = 15×∠AOF Transitive property
15×∠AOF = 120°
∠AOF = 120°/15 = 8°
Given that OE bisects ∠AOD, we have;
∠AOE ≅ ∠DOE Angles bisected by a line
From;
∠AOE = 2×∠AOF, we have; Given
Therefore;
∠AOE = ∠DOE = 2×∠AOF = 2×8° = 16°
∠DOE = 16°.
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Answer:
option: B () is correct.
Step-by-step explanation:
We are given the solution set as seen from the graph as:
(-4,2)
1)
On solving the first inequality we have:
On using the method of splitting the middle term we have:
⇒
⇒
And we know that the product of two quantities are negative if either one of them is negative so we have two cases:
case 1:
and
i.e. x>-2 and x<4
so we have the region as:
(-2,4)
Case 2:
and
i.e. x<-2 and x>4
Hence, we did not get a common region.
Hence from both the cases we did not get the required region.
Hence, option 1 is incorrect.
2)
We are given the second inequality as:
On using the method of splitting the middle term we have:
⇒
⇒
And we know that the product of two quantities are negative if either one of them is negative so we have two cases:
case 1:
and
i.e. x>2 and x<-4
Hence, we do not get a common region.
Case 2:
and
i.e. x<2 and x>-4
Hence the common region is (-4,2) which is same as the given option.
Hence, option B is correct.
3)
On using the method of splitting the middle term we have:
⇒
⇒
And we know that the product of two quantities are positive if either both of them are negative or both of them are positive so we have two cases:
Case 1:
and
i.e. x>-2 and x>4
Hence, the common region is (4,∞)
Case 2:
and
i.e. x<-2 and x<4
Hence, the common region is: (-∞,-2)
Hence, from both the cases we did not get the desired answer.
Hence, option C is incorrect.
4)
On using the method of splitting the middle term we have:
⇒
⇒
And we know that the product of two quantities are positive if either both of them are negative or both of them are positive so we have two cases:
Case 1:
and
i.e. x<2 and x<-4
Hence, the common region is: (-∞,-4)
Case 2:
and
i.e. x>2 and x>-4.
Hence, the common region is: (2,∞)
Hence from both the case we do not have the desired region.
Hence, option D is incorrect.
