Quadrilateral Geometry 2
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Question 1 of 4
1. Question
Find the value of `x`
- `x=` (4)
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The sum of the interior angles in a quadrilateral is `360°`Since the interior angles of a quadrilateral add to `360°,` add the angle measures and set their sum to `360°.` Then, solve for `x`.`30x-2+62+62+118` `=` `360` `30x+240` `=` `360` Simplify `30x+240` `-240` `=` `360` `-240` Subtract `240` from both sides `30x` `=` `120` `30x``divide30` `=` `120``divide30` Divide both sides by `30` `x` `=` `4` `x=4` -
Question 2 of 4
2. Question
Find the value of `x`
- `x=` (105)`°`
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Supplementary angles are when two angles have a sum of `180°.` Typically, these angles lie on a straight line.Opposite angles of a parallelogram have equal values.Find the missing supplementary angle, which is equal to the value of `x`.First, we can see from the diagram that the exterior angle `75°` and the interior angle `/_ADC` lie on a straight line. Therefore, they are supplementary angles
Since supplementary angles add to `180°,` add the angle measures and set their sum to `180°.` Then, solve for the value of `a`.`/_ADC+75` `=` `180` `/_ADC+75` `-75` `=` `180` `-75` Subtract `75` from both sides `/_ADC` `=` `105°` Finally, the angle `/_ADC` is opposite to angle `x`
Since opposite angles on a parallelogram are equal, `/_ x=105°``/_ x=105°` -
Question 3 of 4
3. Question
Find the value of `a`, `b`, and `c`
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`a=` (113)`°``b=` (35)`°``c=` (32)`°`
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Alternate Angles are equal.The sum of the interior angles in a triangle is `180°`Opposite angles of a parallelogram have equal values.First, we can see from the diagram that `35°` and `b` are alternate angles, which means they are equal
Therefore, `/_ b=``35°`Next, since the interior angles of a triangle add to `180°,` add the angle measures and set their sum to `180°.` Then, solve for `c`.`b+c+113` `=` `180` `35+c+113` `=` `180` Plug in the known values `c+148` `=` `180` Simplify `c+148` `-148` `=` `180` `-148` Subtract `148` from both sides `/_ c` `=` `32°` Finally, the angle `113°` is opposite to angle `a`
Since opposite angles on a parallelogram are equal, `/_ a=``113°``/_ a=113°``/_ b=35°``/_ c=32°` -
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Question 4 of 4
4. Question
Find the value of `/_BED`
- `/_BED=` (57)`°`
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An Isosceles Triangle has two congruent sides (the two sides with dashes) and the two base angles are equal.Supplementary angles are when two angles have a sum of `180°.` Typically, these angles lie on a straight line.The sum of the interior angles in a quadrilateral is `360°`To solve for `/_BED`, first find `/_EBC`. Add these two angles to the two given interior angles, then set their sum to `360°`First, since the base angles in an isosceles triangle are equal, `/_ABE` is equal to `70°``/_ABE` `=` `70°` 
Next, we can see from the diagram that the angle `/_ABE` and the angle `/_EBC` lie on a straight line. Therefore, they are supplementary angles
Since supplementary angles add to `180°,` add the angle measures and set their sum to `180°.` Then, solve for the value of `/_EBC`.`/_EBC+/_ABE` `=` `180` `/_EBC+70` `=` `180` Plug in the known values `/_EBC+70` `-70` `=` `180` `-70` Subtract `70` from both sides `/_EBC` `=` `110°` Finally, since the interior angles of a quadrilateral add to `360°,` add the angle measures and set their sum to `360°.` Then, solve for `/_BED`.`/_BED+/_EBC+109+84` `=` `360` `/_BED+110+109+84` `=` `360` Plug in the known lengths `/_BED+303` `=` `360` Simplify `/_BED+303` `-303` `=` `360` `-303` Subtract `303` from both sides `/_BED` `=` `57°` `/_ BED=57°`
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