Grade 8

Theory:

Finding the Fourth Angle of a Quadrilateral

The sum of the interior angles of a quadrilateral is equal to 360^o. To find the fourth angle of a quadrilateral when the other three angles are known, subtract the number of degrees of the other three angles from 360^o.

Example: How many degrees are in the fourth angle of a quadrilateral whose other three angles are 80^o and 110^o and 95^o? Answer: 360^o - 80^o - 110^o - 95^o = 75^o

Solutions from the Previous Issue:

1. You were supposed to add A and B. By accident, you subtracted B from A and got 4. This number is different from the correct answer by 12.What is A?

Solution:

A - B = 4 and
A + B = 16

Note that: B = A - 4

Substitute (A - 4) for B:

A + B = 16
A + (A - 4) = 16
A + A = 16 + 4
2A = 20
A = 10

2. You were supposed to add A and B. But, by mistake you subtracted B from A and got 66. This number is 1/3 of the correct answer.

What is B?

Solution:

We have:

A + B = 66 x 3 = 198
A - B = 66

Note that: A = B + 66

Substitute (B + 66) for A:
A + B = 198
(B + 66) + B = 198
B + B = 198 - 66
2B = 132
B = 66

3. Peter, Gary and Kevin shared $50. The ratio of the amount Peter received and the total amount shared by Gary and Kevin was 3:2. Gary received $4 more than Kevin. How much did Kevin receive?

Solution:

When you divide 50 by 5, and multiply by 2, you will have the total amount shared by Gary and Kevin.

Gary + Kevin = ($50 / 5) x 2 = $20

Also, Gary received $4 more than Kevin.

Gary = Kevin + $4

Substitute (Kevin + $4) for Gary's amount:

Gary + Kevin = $20
(Kevin + $4) + Kevin = $20
Kevin + Kevin = $20 - $4
2 Kevin = $16
Therefore, Kevin (or Kevin's amount) receive $8

Gary receive $8 +$4 = $12

Peter receive $40

4. Boys V, W, X, Y and Z went fishing. V caught 8 more fish than Z.
W caught 20, while X and Y caught 24 and 18 respectively. They caught an average of 20 fish. How many fish did V catch?

Solution:

When you multiply 20 (the average) by 5, you get the total fish caught.

They caught a total of 100 fish based on the average of 20 fish each. Subtract 20, 24 and 18 from 100 to get 38. This is the total of V and Z's catch.

Z + V = 38

Also, V caught 8 more fish than Z:

Z = V - 8

Substitute:
Z + V = 38
(V - 8) + V = 38
2 V = 46
V = 23

Proposed Exercises:

Simplify.

1. (9w^-3)(10w²)(11w^-5)

2. (-12b^-4i^-4)(-5b^-4i⁴)

3. (4l^-5)(3l^-4a⁴)

4. (-8x^-4o⁴)(8x⁴o⁴)

5. (-9c³)(-2c⁵)