Help with Geometry question?

Question

Hello, we're doing Isoceles triangles and I'm confused. LOL
They are telling us to solve these. Did I do the first one right?
And is there a way I can recheck my answer like in algebra by "backtracking" my answer - is that possible in geometry?


They're telling us Find the value of X

4x-20=3x
4x-20+20=3x+20
4x=3x+20
x=20

the answer I got was: x = 20
is that right?


Im lost with this one.

2.) x° 28°
3.) 3x - 6, x + 10
4) 5x° 2x°
5) 4x + 2, 60°, 6x - 30

Sorry I have no way of putting the triangle pictures in here.
Any help breaking these down to solve x is appreciated!

thanks!

#3)
28°
*
-* *-
* *
*x° *
********



#4)


*5° *
* */ \\* *
* * * *
* *2° *
* * * *
* *\ //* *
* *


#5)

*
* * *
* *60°*
* * * 6x - 30
4x +2 \* *
* \ *
* * *
* * *
*)***************( *

Answer 1

In order to answer this question I have to assume the information you are giving us is in different corners of a triangle they have shown you. since it is an isoceles two of the angles are equal and the other angle is equal to 180 - the other two angles (3 inside angles of a triangle add upto 180). You should be able to tell which angles are the same by looking at it, so for example in question 5, you are actually dealing with an equilateral triangle, since if it is isoceles at least 2 of the angles have to be equal. therefore
4x+2+6x-30=180-60
10x-28=120
10x=148
x=14.8

To check your work, you would insert the value of x for each equation, add the three numbers and you should come up with 180.

For question 2 if x is the angle which is equal to the other unknown angle then
x=(180-28)/2
x=152/2
x=76

if x is the third angle (so the other unknown is equal to 28) then
x=180-(28x2)
x=180-56
x=124

Again without the pictures that is as clear as I can be since I am having to guess at the question, I hope this helps

Answer 2

The answer to the first question is correct. To solve the others, just remember that the sum of the angles in a triangle always equals 180 degrees. I am guessing that what they want you to do is find an angle given two other angles.

2. A = 180 - (x + 28)

3. A = 180 - [(3x - 6) + (x + 10)] = 180 - 4x - 4 = 180 - 4(x + 1)

4. A = 180 - (5x + 2x) = 180 - 7x

5. Here you are given three angles, letting you actually find x.

180 = (4x + 2) + 60 + (6x - 30)
180 = 10x - 28 + 60
180 = 10x + 32
148 = 10x
148/10 = 74/5 = x

Now plug 74/5 into both the expressions containing the variable to find the degree measure of each of those angles.

4(74/5) + 2 = (296 + 10)/5 = 306/5 = 61.2 degrees

6(74/5) - 30 = (444 - 150)/5 = 294/5 = 58.8 degrees

As a check, add them all up:

61.2 + 60.0 + 58.8 = 180.0

Answer 3

OK, the first one is right.

Put in 20 for x and you get 4(20) - 20 = 3 (20). 80 - 20 = 60. Check.

2. 28º is either one of the two equal angles or the third angle. That gives you x + 2 (28) = 180 or 2x + 28 = 180.

3. same thing here, two scenarios: (3x-6) + 2 (x+10) = 180 or 2 (3x - 6) + (x + 10) = 180.

4. more of the same

5. One angle is 60; the other two must also be 60; this is a regular or equilateral triangle. 4x + 2 = 60. 6x - 30 = 60. I'd say x = 15, but that doesn't jive with 4x + 2 = 60.

Maybe I'm not understanding the question.

Answer 4

The first answer is correct.

2). in the picture, is this an isoceles right triangle? (is there a little square in the corner of the third angle?). If so, then x+28=90;
x= 90-28=62

3) also assuming isocelese right triangle in the picture
3x-6 + x+10 = 90
4x +4 = 90
4x = 86
x = 21.5
Angles are 57.5 and 32.5

4) again assuming isocelese right triangle in the picture
5x + 2x = 90
7x = 90
x = 12 6/7
Angles are 64 2/7 and 25 5/7

5) Three angles are shown and one is 60, so
4x+2 + 6x-30 = 180-60
10x - 28 = 120
10x = 148
x = 14.8
Angles are 61.2, 60, and 58.8

Answer 5

20 looks right. The others don't make sense to me. There is not enough information.