#6
Vertical angles are the angles opposite each other when two lines cross.
Let's see which angle forms a "X" with ∠EOD:
So, ∠COF is "vertical" with ∠EOD.
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#7
When 2 angles add up to 90 degrees, we say that they are complementary angles.
Since ∠POF + ∠FOB = 90, then ∠POF is complementary to ∠FOB.
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#8
∠BOC + ∠AOC is a straight angle (straight line).
A straight angle is 180 degrees.
So, we can write,
[tex]\angle BOC+\angle AOC=180\degree[/tex]
We know ∠BOC = 150, so ∠AOC will be,
[tex]\begin{gathered} 150\degree+\angle AOC=180\degree \\ \angle\text{AOC}=180-150 \\ \angle\text{AOC}=30\degree \end{gathered}[/tex]
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#9
From the diagram, we can see that ∠EOA and ∠FOB are vertical angles. Thus, they are equal.
Since ∠EOA = 37,
∠FOB = 37
Now, from the diagram, we can see,
∠FOA + ∠FOB = 180 [since they are straight line]
Now, we can easily find ∠FOA:
[tex]\begin{gathered} \angle FOA+\angle FOB=180 \\ \angle\text{FOA}+37=180 \\ \angle\text{FOA}=180-37 \\ \angle\text{FOA}=143\degree \end{gathered}[/tex]
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#10
Adjacent angles are two angles that have a common side and a common vertex (corner point) but do not overlap in any way.
For example,
∠1 and ∠2 are adjacent angles.
From our diagram,
∠HGO is adjacent to ∠EGH
From the diagram above, we see that G is the common vertex and GH is the common side.
Thus,
∠HGO is adjacent to ∠EGH
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#11
From the diagram, we see that ∠EGH and ∠HGO fall in a straight line. So, they add up to 180 degrees.
[tex]\angle\text{EGH}+\angle\text{HGO}=180[/tex]
Given,
∠HGO = 128,
Let's find ∠EGH:
[tex]\begin{gathered} \angle\text{EGH}+\angle\text{HGO}=180 \\ \angle\text{EGH}+128=180 \\ \angle\text{EGH}=180-128 \\ \angle\text{EGH}=52\degree \end{gathered}[/tex]
Given,
[tex]\angle\text{EGH}\cong\angle\text{DOB}[/tex]
We can say:
[tex]\angle\text{DOB}=52\degree[/tex]
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#12
From the figure, we see that ∠EOA + ∠EOD + ∠DOB = 180 degrees [straight line].
Given,
∠EOA = 67
∠DOB = 29
We can solve for ∠EOD:
[tex]\begin{gathered} \angle EOA+\angle EOD+\angle DOB=180 \\ 67+\angle\text{EOD}+29=180 \\ 96+\angle\text{EOD}=180 \\ \angle\text{EOD}=180-96 \\ \angle\text{EOD}=84\degree \end{gathered}[/tex]
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#13
When 2 angles add up to 180 degrees, we say that they are supplementary angles.
Given,
∠AOD + ∠DOB = 180
We can say that ∠AOD is supplementary to ∠DOB.
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#14
Since ∠COF is congruent to ∠DOF and fall is a straight line, we can say that they are each 90 degrees.
Thus, FO and CD will be perpendicular to each other.
So, we can say,
FO is perpendicular to CD
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#15
Given,
∠COP = 72 and ∠POF = 31, we have:
We want to know the measure of ∠EOD.
Let's see below:
We see that ∠COF and ∠EOD are vertical angles.
Vertical angles are equal.
So,
∠EOD = ∠COP + ∠POF
∠EOD = 72 + 31
∠EOD = 103°
'~'-.,__,.-'~'-.,__,.-'~'-.,__,.-'~'-.,__,.-'~'-.,__,.-'~'-.,__,.-'~'-.,__,.-'~'-.,__,.-'~'-.,__,.-
Answers[tex]\begin{gathered} 6.\angle\text{COF} \\ 7.\text{Complementary} \\ 8.\angle\text{AOC}=30\degree \\ 9.\angle\text{FOA}=143\degree \\ 10.\angle\text{HGO} \\ 11.\angle\text{DOB}=52\degree \\ 12.\angle\text{EOD}=84\degree \\ 13.Supplementary \\ 14.Perpendicular \\ 15.\angle\text{EOD}=103\degree \end{gathered}[/tex]
