Equation Problems (Geometry) 1

Topics

Algebra 1

Equations

Equation Problems (Geometry)

Equation Problems (Geometry) 1

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Question 1 of 5

1. Question
Find $x$ $x$
- $x =$ $x=$ (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 $90 °$ $90°$ .

Form an equation knowing that the two smaller angles are complementary and add up to $90 °$ $90°$ .

Right Angle $= 90 °$ $=90°$

Small Angle $1 = 4 x °$ $1=4x°$

Small Angle $2 = 46 °$ $2=46°$

Small Angle $1$ $1$ $+$ $+$ Small Angle $2$ $2$ $=$ $=$ Right Angle

$4 x$ $4x$ $+$ $+$ $46$ $46$ $=$ $=$ $90$ $90$ Substitute the values

To solve for $x$ $x$ , it needs to be alone on one side.

Start by moving $46$ $46$ to the other side by subtracting $46$ $46$ from both sides of the equation.

$4$ $4$ $x$ $x$ $+ 46$ $+46$ $=$ $=$ $90$ $90$

$4$ $4$ $x$ $x$ $+ 46$ $+46$ $- 46$ $-46$ $=$ $=$ $90$ $90$ $- 46$ $-46$

$4$ $4$ $x$ $x$ $=$ $=$ $44$ $44$ $46 - 46$ $46-46$ cancels out

Finally, remove $4$ $4$ by dividing both sides of the equation by $4$ $4$ .

$4$ $4$ $x$ $x$ $=$ $=$ $44$ $44$

$4$ $4$ $x$ $x$ $\div 4$ $divide4$ $=$ $=$ $44$ $44$ $\div 4$ $divide4$

$x$ $x$ $=$ $=$ $11$ $11$ $4 \div 4$ $4divide4$ cancels out

Check our work

To confirm our answer, substitute $x = 11$ $x=11$ to the formed equation.

$4 x + 46$ $4x+46$ $=$ $=$ $90$ $90$

$4 (11) + 46$ $4(11)+46$ $=$ $=$ $90$ $90$ Substitute $x = 11$ $x=11$

$44 + 46$ $44+46$ $=$ $=$ $90$ $90$

$90$ $90$ $=$ $=$ $90$ $90$

Since the equation is true, the answer is correct.

$x = 11$ $x=11$
Question 2 of 5

2. Question
Find $x$ $x$
- $x =$ $x=$ (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 $180 °$ $180°$ .

Form an equation knowing that the two smaller angles are supplementary and add up to $180 °$ $180°$ .

Straight Angle $= 180 °$ $=180°$

Small Angle $1 = 148 °$ $1=148°$

Small Angle $2 = 2 x °$ $2=2x°$

Small Angle $1$ $1$ $+$ $+$ Small Angle $2$ $2$ $=$ $=$ Straight Angle

$148$ $148$ $+$ $+$ $2 x$ $2x$ $=$ $=$ $180$ $180$ Substitute the values

$2 x + 148$ $2x+148$ $=$ $=$ $180$ $180$

To solve for $x$ $x$ , it needs to be alone on one side.

Start by moving $148$ $148$ to the other side by subtracting $148$ $148$ from both sides of the equation.

$2$ $2$ $x$ $x$ $+ 148$ $+148$ $=$ $=$ $180$ $180$

$2$ $2$ $x$ $x$ $+ 148$ $+148$ $- 148$ $-148$ $=$ $=$ $180$ $180$ $- 148$ $-148$

$2$ $2$ $x$ $x$ $=$ $=$ $32$ $32$ $148 - 148$ $148-148$ cancels out

Finally, remove $2$ $2$ by dividing both sides of the equation by $2$ $2$ .

$2$ $2$ $x$ $x$ $=$ $=$ $32$ $32$

$2$ $2$ $x$ $x$ $\div 2$ $divide2$ $=$ $=$ $32$ $32$ $\div 2$ $divide2$

$x$ $x$ $=$ $=$ $16$ $16$ $2 \div 2$ $2divide2$ cancels out

Check our work

To confirm our answer, substitute $x = 16$ $x=16$ to the formed equation.

$2 x + 148$ $2x+148$ $=$ $=$ $180$ $180$

$2 (16) + 148$ $2(16)+148$ $=$ $=$ $180$ $180$ Substitute $x = 16$ $x=16$

$32 + 148$ $32+148$ $=$ $=$ $180$ $180$

$180$ $180$ $=$ $=$ $180$ $180$

Since the equation is true, the answer is correct.

$x = 16$ $x=16$

Question 3 of 5

Find

x

$x$

$x =$ $x=$ (28)

Question 4 of 5

4. Question
Find $x$ $x$
- $x =$ $x=$ (80)
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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.

$2 x - 30$ $2x-30$ $=$ $=$ $x + 50$ $x+50$

To solve for $x$ $x$ , it needs to be alone on one side.

Start by moving $x$ $x$ to the other side by subtracting $x$ $x$ from both sides of the equation.

$2$ $2$ $x$ $x$ $- 30$ $-30$ $=$ $=$ $x$ $x$ $+ 50$ $+50$

$2$ $2$ $x$ $x$ $- 30$ $-30$ $- x$ $-x$ $=$ $=$ $x$ $x$ $+ 50$ $+50$ $- x$ $-x$

$x$ $x$ $- 30$ $-30$ $=$ $=$ $50$ $50$ $x - x$ $x-x$ cancels out

Finally, move $30$ $30$ to the other side by adding $30$ $30$ to both sides of the equation.

$x$ $x$ $- 30$ $-30$ $=$ $=$ $50$ $50$

$x$ $x$ $- 30$ $-30$ $+ 30$ $+30$ $=$ $=$ $50$ $50$ $+ 30$ $+30$

$x$ $=$ $80$ $-30+30$ cancels out

Check our work

To confirm our answer, substitute $x=80$ to the formed equation.

$2x-30$ $=$ $x+50$

$2(80)-30$ $=$ $80+50$ Substitute $x=80$

$160-30$ $=$ $130$

$130$ $=$ $130$

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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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.

$5$ $x$ $+40$ $=$ $360$

$5$ $x$ $+40$ $-40$ $=$ $360$ $-40$

$5$ $x$ $=$ $320$ $40-40$ 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 work

To 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.

$x=64$

$5$ $5$ $x$ $x$ $+ 40$ $+40$	$=$ $=$	$180$ $180$
$5$ $5$ $x$ $x$ $+ 40$ $+40$ $- 40$ $-40$	$=$ $=$	$180$ $180$ $- 40$ $-40$
$5$ $5$ $x$ $x$	$=$ $=$	$140$ $140$	$40 - 40$ $40-40$ cancels out

$5$ $5$ $x$ $x$	$=$ $=$	$140$ $140$
$5$ $5$ $x$ $x$ $\div 5$ $divide5$	$=$ $=$	$140$ $140$ $\div 5$ $divide5$
$x$ $x$	$=$ $=$	$28$ $28$	$5 \div 5$ $5divide5$ cancels out

Equation Problems (Geometry) 1

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Quiz summary

Information

1. Question

Hint

Great Work!

Inverse Operations

2. Question

Hint

Good Job!

Inverse Operations

3. Question

Hint

Well Done!

Inverse Operations

4. Question

Hint

Fantastic!

Inverse Operations

Vertically Opposite Angles

Alternate Angles

Corresponding Angles

5. Question

Hint

Excellent!

Inverse Operations

Quizzes

Small Angle $1$ $1$ $+$ $+$ Small Angle $2$ $2$	$=$ $=$	Right Angle
$4 x$ $4x$ $+$ $+$ $46$ $46$	$=$ $=$	$90$ $90$	Substitute the values

$4$ $4$ $x$ $x$ $+ 46$ $+46$	$=$ $=$	$90$ $90$
$4$ $4$ $x$ $x$ $+ 46$ $+46$ $- 46$ $-46$	$=$ $=$	$90$ $90$ $- 46$ $-46$
$4$ $4$ $x$ $x$	$=$ $=$	$44$ $44$	$46 - 46$ $46-46$ cancels out

$4 x + 46$ $4x+46$	$=$ $=$	$90$ $90$
$4 (11) + 46$ $4(11)+46$	$=$ $=$	$90$ $90$	Substitute $x = 11$ $x=11$
$44 + 46$ $44+46$	$=$ $=$	$90$ $90$
$90$ $90$	$=$ $=$	$90$ $90$

Small Angle $1$ $1$ $+$ $+$ Small Angle $2$ $2$	$=$ $=$	Straight Angle
$148$ $148$ $+$ $+$ $2 x$ $2x$	$=$ $=$	$180$ $180$	Substitute the values
$2 x + 148$ $2x+148$	$=$ $=$	$180$ $180$

$2$ $2$ $x$ $x$ $+ 148$ $+148$	$=$ $=$	$180$ $180$
$2$ $2$ $x$ $x$ $+ 148$ $+148$ $- 148$ $-148$	$=$ $=$	$180$ $180$ $- 148$ $-148$
$2$ $2$ $x$ $x$	$=$ $=$	$32$ $32$	$148 - 148$ $148-148$ cancels out

Angle $1$ $1$ $+$ $+$ Angle $2$ $2$ $+$ $+$ Angle $3$ $3$	$=$ $=$	Straight Angle
$50$ $50$ $+$ $+$ $3 x$ $3x$ $+$ $+$ $(2 x - 10)$ $(2x-10)$	$=$ $=$	$180$ $180$	Substitute the values
$5 x + 40$ $5x+40$	$=$ $=$	$180$ $180$	Simplify

$50 + 3 x + (2 x - 10)$ $50+3x+(2x-10)$	$=$ $=$	$180$ $180$
$50 + 3 (28) + (2 (28) - 10)$ $50+3(28)+(2(28)-10)$	$=$ $=$	$180$ $180$	Substitute $x = 28$ $x=28$
$50 + 84 + (56 - 10)$ $50+84+(56-10)$	$=$ $=$	$180$ $180$
$50 + 84 + 46$ $50+84+46$	$=$ $=$	$180$ $180$
$180$ $180$	$=$ $=$	$180$ $180$

$2$ $2$ $x$ $x$ $- 30$ $-30$	$=$ $=$	$x$ $x$ $+ 50$ $+50$
$2$ $2$ $x$ $x$ $- 30$ $-30$ $- x$ $-x$	$=$ $=$	$x$ $x$ $+ 50$ $+50$ $- x$ $-x$
$x$ $x$ $- 30$ $-30$	$=$ $=$	$50$ $50$	$x - x$ $x-x$ cancels out

$2x-30$	$=$	$x+50$
$2(80)-30$	$=$	$80+50$	Substitute $x=80$
$160-30$	$=$	$130$
$130$	$=$	$130$

Angle $1$ $+$ Angle $2$ $+$ Angle $3$	$=$	Revolution
$x$ $+$ $3x$ $+$ $(x+40)$	$=$	$360$	Substitute the values
$5x+40$	$=$	$360$	Simplify

$5$ $x$ $+40$	$=$	$360$
$5$ $x$ $+40$ $-40$	$=$	$360$ $-40$
$5$ $x$	$=$	$320$	$40-40$ cancels out

$5$ $x$	$=$	$320$
$5$ $x$ $divide5$	$=$	$320$ $divide5$
$x$	$=$	$64$	$5divide5$ cancels out

$x+3x+(x+40)$	$=$	$360$
$64+3(64)+(64+40)$	$=$	$360$	Substitute $x=64$
$64+192+104$	$=$	$360$
$360$	$=$	$360$