Angles and Parallel Lines
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Question 1 of 4
1. Question
Find the value of `x`
- `x=` (58)`°`
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Vertically Opposite Angles
Corresponding Angles
Co-Interior 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°``/_ x=58°` -
Question 2 of 4
2. Question
Find the value of `a`
- `a=` (100)`°`
Hint
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Alternate Angles
Corresponding Angles
Co-Interior Angles
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 revolutionSince 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°` `/_ a=100°` -
Question 3 of 4
3. Question
Find the value of `x`
- `x=` (85)`°`
Hint
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Alternate Angles
Corresponding Angles
Co-Interior Angles
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
Therefore, `/_ x=85°``/_ x=85°` -
Question 4 of 4
4. Question
Find the value of `k`
- `k=` (250)`°`
Hint
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Incorrect
Alternate Angles
Corresponding Angles
Co-Interior Angles
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°` `/_ k=250°`
Quizzes
- Complementary and Supplementary Angles 1
- Complementary and Supplementary Angles 2
- Complementary and Supplementary Angles 3
- Vertical, Revolution and Reflex Angles 1
- Vertical, Revolution and Reflex Angles 2
- Alternate, Corresponding and Co-Interior Angles 1
- Alternate, Corresponding and Co-Interior Angles 2
- Alternate, Corresponding and Co-Interior Angles 3
- Angles and Parallel Lines
- Triangle Geometry 1
- Triangle Geometry 2
- Triangle Geometry 3
- Quadrilateral Geometry 1
- Quadrilateral Geometry 2