Equation Problems (Geometry) 1
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Question 1 of 5
1. Question
Find `x` `x=` (11)
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Notice that the full angle has a square marker, which means it is a right angle and measures `90°`.Form an equation knowing that the two smaller angles are complementary and add up to `90°`.Right Angle`=90°`Small Angle `1=4x°`Small Angle `2=46°`Small Angle `1` `+`Small Angle `2` `=` Right Angle `4x` `+``46` `=` `90` Substitute the values To solve for `x`, it needs to be alone on one side.Start by moving `46` to the other side by subtracting `46` from both sides of the equation.`4``x` `+46` `=` `90` `4``x` `+46` `46` `=` `90` `46` `4``x` `=` `44` `4646` cancels out Finally, remove `4` by dividing both sides of the equation by `4`.`4``x` `=` `44` `4``x``divide4` `=` `44``divide4` `x` `=` `11` `4divide4` cancels out Check our workTo confirm our answer, substitute `x=11` to the formed equation.`4x+46` `=` `90` `4(11)+46` `=` `90` Substitute `x=11` `44+46` `=` `90` `90` `=` `90` Since the equation is true, the answer is correct.`x=11` 
Question 2 of 5
2. Question
Find `x` `x=` (16)
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.A straight angle measures `180°`.Form an equation knowing that the two smaller angles are supplementary and add up to `180°`.Straight Angle`=180°`Small Angle `1=148°`Small Angle `2=2x°`Small Angle `1` `+`Small Angle `2` `=` Straight Angle `148` `+``2x` `=` `180` Substitute the values `2x+148` `=` `180` To solve for `x`, it needs to be alone on one side.Start by moving `148` to the other side by subtracting `148` from both sides of the equation.`2``x` `+148` `=` `180` `2``x` `+148` `148` `=` `180` `148` `2``x` `=` `32` `148148` cancels out Finally, remove `2` by dividing both sides of the equation by `2`.`2``x` `=` `32` `2``x``divide2` `=` `32``divide2` `x` `=` `16` `2divide2` cancels out Check our workTo confirm our answer, substitute `x=16` to the formed equation.`2x+148` `=` `180` `2(16)+148` `=` `180` Substitute `x=16` `32+148` `=` `180` `180` `=` `180` Since the equation is true, the answer is correct.`x=16` 
Question 3 of 5
3. Question
Find `x` `x=` (28)
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.A straight angle measures `180°`.Form an equation knowing that the three angles are supplementary and add up to `180°`.Straight Angle`=180°`Angle `1=50°`Angle `2=3x°`Angle `3=(2x10)°`Angle `1` `+`Angle `2` `+`Angle `3` `=` Straight Angle `50` `+``3x` `+``(2x10)` `=` `180` Substitute the values `5x+40` `=` `180` Simplify To solve for `x`, it needs to be alone on one side.Start by moving `40` to the other side by subtracting `40` from both sides of the equation.`5``x` `+40` `=` `180` `5``x` `+40` `40` `=` `180` `40` `5``x` `=` `140` `4040` cancels out Finally, remove `5` by dividing both sides of the equation by `5`.`5``x` `=` `140` `5``x``divide5` `=` `140``divide5` `x` `=` `28` `5divide5` cancels out Check our workTo confirm our answer, substitute `x=28` to the formed equation.`50+3x+(2x10)` `=` `180` `50+3(28)+(2(28)10)` `=` `180` Substitute `x=28` `50+84+(5610)` `=` `180` `50+84+46` `=` `180` `180` `=` `180` Since the equation is true, the answer is correct.`x=28` 
Question 4 of 5
4. Question
Find `x` `x=` (80)
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Fantastic!
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.Vertically Opposite Angles
Alternate Angles
Corresponding Angles
Form an equation knowing that vertically opposite angles are equal.`2x30` `=` `x+50` To solve for `x`, it needs to be alone on one side.Start by moving `x` to the other side by subtracting `x` from both sides of the equation.`2``x` `30` `=` `x` `+50` `2``x` `30` `x` `=` `x` `+50` `x` `x` `30` `=` `50` `xx` cancels out Finally, move `30` to the other side by adding `30` to both sides of the equation.`x` `30` `=` `50` `x` `30` `+30` `=` `50` `+30` `x` `=` `80` `30+30` cancels out Check our workTo confirm our answer, substitute `x=80` to the formed equation.`2x30` `=` `x+50` `2(80)30` `=` `80+50` Substitute `x=80` `16030` `=` `130` `130` `=` `130` Since the equation is true, the answer is correct.`x=80` 
Question 5 of 5
5. Question
Find `x` `x=` (64)
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Excellent!
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Inverse Operations
When moving a term to the other side of an equation, the operation is inversed.A revolution measures `360°`.Form an equation knowing that the three angles form a revolution.Revolution`=360°`Angle `1=x°`Angle `2=3x°`Angle `3=(x+40)°`Angle `1` `+`Angle `2` `+`Angle `3` `=` Revolution `x` `+``3x` `+``(x+40)` `=` `360` Substitute the values `5x+40` `=` `360` Simplify To solve for `x`, it needs to be alone on one side.Start by moving `40` to the other side by subtracting `40` from both sides of the equation.`5``x` `+40` `=` `360` `5``x` `+40` `40` `=` `360` `40` `5``x` `=` `320` `4040` cancels out Finally, remove `5` by dividing both sides of the equation by `5`.`5``x` `=` `320` `5``x``divide5` `=` `320``divide5` `x` `=` `64` `5divide5` cancels out Check our workTo confirm our answer, substitute `x=64` to the formed equation.`x+3x+(x+40)` `=` `360` `64+3(64)+(64+40)` `=` `360` Substitute `x=64` `64+192+104` `=` `360` `360` `=` `360` Since the equation is true, the answer is correct.`x=64`
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