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Geometry question...?

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I'm stumped cause my geometry teacher didn't teach my class a certain part of the lesson and i need help. and if you could, try to explain how to do the work so that i know when it comes time for a test. Thanks!

1. The measures of two complementary angles are 16z-9 and 4z+ 3. Find the measures of the angles

2.The measure of angle 1 is five less than four times the measure of angle 2. If angle 1 and angle 2 form a linear pair, what are their measures?

3.( you might have trouble with this one because there is a diagram your supposed to look at) If m angle AFB = 8x-6 and m angle BFC = 14x+ 8, find the value of x so that angle AFC is a right angle

4. angle L and angle M are complementary angles. angle N and angles P are complementary angles If m angle L = y-2, m angle M = 2x+3, m angle N =2x-y, and m angle P = x- 1, find the values of x, y, m angle L, m angle M, m angle N, and m angle P.

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  1. First some definitions:

    If two angles are complementary, or form a right angle, that means they add up to 90°

    If two angles are supplementary, or form a linear pair, that means they add up to 180°

    Use this knowledge to solve each problem.

    PROBLEM 1:

    Angles are complementary (add to 90°):

    (16z - 9) + (4z + 3) = 90

    20z - 6 = 90

    20z = 96

    z = 96/20

    z = 4.8

    Plug the value of z back into the equation for each angle.

    Angle 1

    16z - 9

    = 16(4.8) - 9

    = 76.8 - 9

    = 67.8°

    Angle 2

    4z + 3

    = 4(4.8) + 3

    = 19.2 + 3

    = 22.2°

    (Double check that these add up to 90°)

    Answer:

    Angle 1 = 67.8°

    Angle 2 = 22.2°

    PROBLEM 2:

    Let A be the measure of angle 1

    Let B be the measure of angle 2

    "Angle 1 is five less than four times the measure of angle 2"

    Angle 1 --> A = 4B - 5

    Angle 2 --> B

    Together they form a linear pair (add to 180°)

    A + B = 180°

    (4B - 5) + B = 180°

    5B - 5 = 180

    5B = 185

    B = 185/5

    B = 37°

    A = 4B - 5

    A = 4(37) - 5

    A = 148 - 5

    A = 143°

    (Again double-check that they add to 180°)

    Answer:

    Angle 1 = 143°

    Angle 2 = 37°

    PROBLEM 3:

    They form a right triangle so they add up to 90°

    (8x - 6) + (14x + 8) = 90

    Use the same method as Problem #1.

    PROBLEM 4:

    Use the same methods except you need to solve for both x and y.  Then use the value to compute the measures for the four angles L, M, N and P.

    I'll get you started:

    L and M are complementary (add to 90°)

    (y - 2) + (2x + 3) = 90

    N and P are complementary (add to 90°)

    (2x - y) + (x - 1) = 90

    First equation:

    y - 2 + 2x + 3 = 90

    y + 2x + 1 = 90

    y + 2x = 89

    Second equation:

    (2x - y) + (x - 1) = 90

    2x - y + x - 1 = 90

    3x - y - 1 = 90

    -y + 3x - 1 = 90

    -y + 3x = 91

    Add these two equations together and the Ys will cancel.

    y + 2x = 89

    -y + 3x = 91

    ----------------

    5x = 180

    x = 180/5

    x = 36

    Now plug in, solve for y.  Finally plug the values of x and/or y into each angle measurement to get L, M, N and P.


  2. for the first one, complementary angles add up to 90 degrees. (16z-9) + (4z+3) = 90. Thus, z = 4.8, and one angle is 67.8 degrees, and the other one is 22.2 degrees.
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