**Read the table and find the conjecture and three quadrilaterals that are different.**

Given: The table

To find The conjecture and three quadrilaterals that are different.

Evaluate to get the required result.

Conjecture: Using the table from part Exploration 1, we can say that the sum of the angle measures of a quadrilateral is equal to 360°.

Upon drawing three other quadrilaterals and measuring their angles, we can conclude that the conjecture we have is TRUE

Conjecture: Using the table from part Exploration 1, we can say that the sum of the angle measures of a quadrilateral is equal to 360°.

Upon drawing three other quadrilaterals and measuring their angles, we can conclude that the conjecture we have is TRUE.

**Evaluate to get the required result and find the value of x. **

Given: The angle

To find: The value of x

Evaluate to get the required result.

Conjecture: The sum of the angle measures of a quadrilateral is equal to 360°.

Add the angle measurements for each quadrilateral and equate it to 360 to obtain the value of x.

85+100+80+x=360

265+x=360

Combine like terms,

265+x−265=360−265

Subtract 265 on both sides,

x=95°

The value of x is 95°

Given: The angle

To find: The value of x

Evaluate to get the required result.

Add the angle measurements for each quadrilateral and equate it to 360 to obtain the value of x.

x+78+72+60=360

x+210=360

Combine like terms

x+210−210=360−210

Subtract 210 on both sides

x=150°

The value of x is x=150°.

Given: The angle

To find: The value of x

Evaluate to get the required result.

Add the angle measurements for each quadrilateral and equate it to 360 to obtain the value of x

90+30+x+90=360

x+210=360

Combine like terms

x+210−210=360−210

Subtract 210 on both sides

x=150°

The value of x is x=150°.

One real-life example of using simple equations is when you are using your money.

When you buy something from a store, you will give your money to pay for it.

If the price is less than your payment, you will have a change.

You can compute your change by subtracting your money from the price of the item.

If you buy an item for a certain quantity, for example, 3 packs of biscuits, the price will be multiplied by the quantity.

The use of simple equations to solve real-life problems is stated.

**Tear off the four corners of the quadrilateral and rearrange them to affirm the conjecture Evaluate to get the required result. Find the conjecture.**

Given: Tear off the four corners of the quadrilateral and rearrange them to affirm the conjecture

To find The conjecture.

Evaluate to get the required result.

Consider that the sum of the angle measures of a quadrilateral is equal to 360 degrees.

The same goes for a circle.

Upon cutting off the corners of the quadrilaterals and rearranging them, it will form a circle.

This proves that the angles will still sum up to 360, proving the conjecture.

The angles will still sum up to 360, proving the conjecture.

**Evaluate the equation w + 4 = 16 and find the equation is true or not.**

Given: The equation w+4=16

To find: If the equation is true or not.

Evaluate to get the required result.

Let us solve for w.

w+4=16

w+4−4=16−4 (Subtract 4 on both sides)

w=12

Substitute the obtained value back to the original equation to verify the solution.

w+4=16

12+4=16

16=16

The equation is true w=12.

**Evaluate the equation -15 + w = 6. Find the value of the variable.**

Given: An equation−15+w=6

To find Value of the variable.

Evaluate to get the answer.

Using the equation, we solve for w

−15+w=6

−15+w+15=6+15 (Add 15 on both sides)

w=21

Substitute the obtained value back to the original equation to verify the solution.

−15+w=6

−15+21

LHS=RHS.

The obtained value for the equation is w=21.

**Evaluate the equation -2 = y – 9. Find the value of the variable.**

Given: An equation−2=y−9

To find Value of the variable.

Evaluate to get the answer.

Using the equation, we solve for y.

−2=y−9

−2+9=y−9+9 (Add 9 on both sides)

y=7.

Substitute the obtained value back to the original equation to verify the solution.

−2=y−9

−2=7−9

−2=−2

LHS= RHS.

The obtained value for the equation is y=7.

**Evaluate the equation 3 = q/11. Find the value of variable.**

Given: An equation 3=q/11.

To find Value of the variable.

Evaluate to get the answer.

Using the equation, we solve for.

3=q/11

3.11=q/11.11 (Multiply 11 on both sides)

33=q.

Substitute the obtained value back to the original equation to verify the solution.

3=q/11

3=33/11

3=3

LHS=RHS.

The obtained value for the equation is q=33.

**Evaluate the equation n/-2 = -15. Find the value of the variable.**

Given: An equation n/−2 =−15.

To find Value of the variable.

Evaluate to get the answer.

Using the equation, we solve for n.

n/−2=−15

n/−2.(−2)=−15.(−2) (Multiply -2 on both sides)

n= 30.

Substitute the obtained value back to the original equation to verify the solution.

n/−2=−15

30/−2=−15

−15=−15

LHS=RHS.

The obtained value for the equation is n=30.