Geometry question...?

Question

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.

Answer 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.

Answer 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.