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Question 1 of 4
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Vertically Opposite Angles
Co-Interior Angles are when two angles have a sum of 180°.
Vertically Opposite Angles are equal.
To solve for x, get the supplementary angle of 122°.
First, we can see from the diagram that 122° and ∠ACD are co-interior angles, which add to 180°
Since co-interior angles add to 180°, add the angle measures and set their sum to 180°. Then, solve for the value of ∠ACD.
| ∠ACD+122 |
= |
180 |
| ∠ACD+122 -122 |
= |
180 -122 |
Subtract 122 from both sides |
| ∠ACD |
= |
58° |
Finally, we can see that angle ∠ACD is vertically opposite to angle x
Since vertically opposite angles are equal, ∠ x=58°
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Question 2 of 4
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Co-Interior Angles are when two angles have a sum of 180°.
A Revolution is when angles meet on a point and have a sum of 360°. Typically, these angles form a circle.
To solve for a, add it to the co-interior angles of 55° and 45°, then set their sum to 360°.
First, we can see from the diagram that 45° and ∠DCE are co-interior angles, which add to 180°
Since co-interior angles add to 180°, add the angle measures and set their sum to 180°. Then, solve for the value of ∠DCE.
| ∠DCE+45 |
= |
180 |
| ∠DCE+45 -45 |
= |
180 -45 |
Subtract 45 from both sides |
| ∠DCE |
= |
135° |
Next, we can see from the diagram that 55° and ∠DCB are co-interior angles, which add to 180°
Since co-interior angles add to 180°, add the angle measures and set their sum to 180°. Then, solve for the value of ∠DCB.
| ∠DCB+55 |
= |
180 |
| ∠DCB+55 -55 |
= |
180 -55 |
Subtract 55 from both sides |
| ∠DCB |
= |
125° |
Angle a,∠DCE, and ∠DCB meet at a point, which makes them a revolution
Since a revolution adds to 360°, add the angle measures and set their sum to 360° in order to solve for a
| a+∠DCE+∠DCB |
= |
360 |
| a+135+125 |
= |
360 |
Plug in the known values |
| a+260 |
= |
360 |
Simplify |
| a+260 -260 |
= |
360 -260 |
Subtract 260 from both sides |
| a |
= |
100° |
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Question 3 of 4
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Co-Interior Angles are when two angles have a sum of 180°.
Alternate Angles are equal.
To solve for x, get the supplementary angle of 95°.
First, we can see from the diagram that 95° and ∠BDC are co-interior angles, which add to 180°
Since co-interior angles add to 180°, add the angle measures and set their sum to 180°. Then, solve for the value of ∠BDC.
| ∠BDC+95 |
= |
180 |
| ∠BDC+95 -95 |
= |
180 -95 |
Subtract 95 from both sides |
| ∠BDC |
= |
85° |
Finally, we can see from the diagram that ∠BDC° and x are alternate angles, which means they are equal
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Question 4 of 4
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Co-Interior Angles are when two angles have a sum of 180°.
To solve for k, add the co-interior angles of 50° and 60°.
First, add an imaginary line to the figure in a way that it is parallel to the two other parallel lines.
Now, we can see from the diagram that 50° and x are co-interior angles, which add to 180°
Since co-interior angles add to 180°, add the angle measures and set their sum to 180°. Then, solve for the value of x.
| x +50 |
= |
180 |
| x +50 -50 |
= |
180 -50 |
Subtract 60 from both sides |
| x |
= |
130° |
Next, we can also see from the diagram that 60° and y are co-interior angles, which add to 180°
Since co-interior angles add to 180°, add the angle measures and set their sum to 180°. Then, solve for the value of y.
| y +60 |
= |
180 |
| y +60 -60 |
= |
180 -60 |
Subtract 60 from both sides |
| y |
= |
120° |
Finally, add the value of x and y to get the value of k
| k |
= |
x+y |
| k |
= |
130+120 |
Plug in the known values |
| k |
= |
250° |
