Geometry Help?

Question

Can someone help me please with these questions? I posted a bulletin before this one on the same problems but they did lack information. So I have scanned the page they assigned us for homework today. I really want to learn this but unfortunately I have a teacher who just rushes through things, and this is not my forte. (math that is) THANKS IN ADVANCE!!!

We have to find the value of X.

I uploaded the scanned picture of the book to tinypic.com.
Can someone please help me? THANK YOU SO MUCH!

http://i16.tinypic.com/48mi8pi.jpg

Answer 1

1. x=20
2. x=8
3. x=76
4. x=15
5. x=16
6. x=10
Just realize when its a triangle with two equal sides or angles, set them equal to each other, and know the angles in a triangle add up to 180.
If you need more description on how to solve, email me

Answer 2

Isoceles triangle - any triangle in which two sides are equal

If two sides of a triangle are equal, then the angles opposite those sides are equal as well. The same applies with an equilateral triangle (each side in the triangle is equal, therefore all the angles in the triangle are equal and thus 60 degrees, as for 180 = 3x, x = 60 degrees).

1. 4x - 20 = 3x so x = 20 degrees



2. 3x - 6 = x + 10 so 2x = 16 so x = 8



3. 28 + 2x = 180 so 2x = 152 so x = 76 degrees (this one is tricky; just remember that the sum of the angles in a triangle is always 180 degrees, and then use what I posted above)



4. (2 * 5x) + 2x = 180 so 10x + 2x = 180 so 12x = 180 so x = 15 degrees (the angle of 2x results from the intersection of those two lines; therefore the angles opposite it in the intersection is also 2x. Now use what I posted above about the sides of triangles)



5. Allright, this is a pyramid with the faces formed by equilateral triangles (note the 60 degree angle which is present in what is an isoceles triangle; 60 + 2x = 180 so those other angles are 60 degrees as well). Therefore, 6x - 30 = 4x + 2 so 2x = 32 so x = 16.



6. A simple isoceles triangle! Just remember what I posted above. . .3x + 10 = 5x - 10 so 2x = 20 so x = 10 degrees.



Please remember to include the degrees sign where I have said "x = ___ degrees"; otherwise, the answer is incorrect.

Answer 3

first notations,

in tick mark or double tick mark or arc drawn in an angle means that the sides or the angles with that mark are equal to each other.

also, the angles of a triangle always add up to 180 degrees.

that being said, let's go:

1. the two single tick lines mean that those two sides are equal to each other so you have an isosceles triangle. in addition to the two sides being equal, the two angles associated with the sides are also equal so,

4x - 20 = 3x or 4x - 3x =20 or x = 20

2. to two arcs drawn in the two angles mean that the angles are equal so again an isosceles triangle, and, as above, the two labeled lines must also be equal, so:

3x - 6 = x + 10 or 3x - x = 10 + 6 or 2x = 16 or x=8

3. another isoscelese triange given the two ticked lines. now, you have to realized that the two angles that equal each other are at the base of the triangle. using the sum of all the angles = 180 you get:

180 = 28 + x + x or 180 - 28 = 2x or 152 = 2x or x = 76

4. now you have two isosceles triangles attached at their vertices. the key here is to recognize that the vertex angle (labeled 2x in the double ticked isosceles triangle) in both triangles are equal by geometry. and the angles at the base of the single ticked triangle are both 5x so,

180 = 2x + 5x + 5x or 180 = 12x or x=15

5. the triangle facing you is an equilateral triangle because the top angle is given as 60 degrees and the two bottom angles are equal to each other, so they must also both be 60 degrees (180 - 60 = x + x or 120 = 2x or x=60. so if all the angles are 60, then all the sides must be equal as well (hence the name equilateral). the triangle on the side is an isosceles triangle by the ticks so:

4x + 2 = 6x - 30 or 2 + 30 = 6x - 4x or 32 = 2x or x = 16

6. another isosceles triangle by the single tick marks. the two base angles must be equal so:

3x + 10 = 5x - 10 or 5x - 3x = 10 + 10 or 2x = 20 or x=10


Hope this helps you understand some of the principles of triangles and geometry.

Answer 4

These problems are dealing with 2 sides of a triangle that are equal (equilateral triangle). So,

1. equilateral triangle property that if 2 sides are equal, then the 2 coresponding angles are also equal. Therefore, you have

(4x - 20) = 3x, and solving for x

x = 20

2. With same property, if 2 angles of a triangle are equal, it makes the 2 sides are equal. So,

3x - 6 = x + 10

x = 8

3. Similarly, because two sides are equal, it's a equilateral triangle, and 2 angles are equal. And the sum of all 3 angles are equal 180. Therefore,

x + x + 28 = 180. Solve for x

4. Look at the picture, we know that the angle adjacent to the angle 2x will be equal to 2x. Also, in equilateral triangle, the two angle are equal if the two sides are equal. And the sum of all three angles are 180. So,

2x + 5x + 5x = 180. Then simplify and solve for x

5. We know the 2 sides of the triangle on the left are equal, and 1 side is equal to 4x + 2. Therefore, the other side is also 4x + 2, and this side is happening to be one of the sides of the triangle on the right which also is a equilateral due to the fact that the two angles are equal. So, the two side are also equal to each other. And we get

4x + 2 = 6x - 30. Then solve for x.

6. Due to the two sides are equal, the two angles are also equal, and,

3x + 10 = 5x - 10. Solve for x

Answer 5

1. This is clearly an isoceles triangle. In an isoceles triangle, note only are two sides the same, but the angles they adjoin to will be the same too. Therefore, the angles will be the same degree, and we can equate them.

4x - 20 = 3x, so
x = 20

2. We have another isoceles triangle. Both sides will be the same, so just equate them.

3x - 6 = x + 10
2x = 16
x = 8

3. We have another isoceles triangle; this time though, the angle given is 28. The angle on one end of the isoceles is x; because the opposite side is the matching side, it follows that the remaining angle is also x.

The sums of the angles of a triangle is ALWAYS 180. Therefore, we add up the angles to make 180.

x + x + 28 = 180
2x = 152
x = 76

4. Here, we have two isoceles triangles. We also have an X; in an X, the opposite angles are always equal.

On the left triangle, we have 5x, so the angle on its matching side should also be 5x. It also follows that, since opposite angles of an X are equal, the third angle will be 2x. Therefore,

5x + 5x + 2x = 180
12x = 180
x = 180/12 = 15

Answer 6

2. Since the two sides of this triangle for which a length is given are equal you can equate the two and solve.

3x-6 = x+10
2x = 16
x = 8

3. This is an isosceles triangle son the two unknown angles are equal to each other. Hence 180 = 28 + x + x

152 =2x
x = 76 degrees

4. Two angles on the triangle on the left are 5x so the third angle is 180-10x. Since the two angles created by the intersection of straight lines are equal you can equate the prior result to the 2x value of the triangle on the right.

180-10x=2x
180 = 12x
x = 15

Answer 7

You'll be able to do these pretty easily if you remember a few rules:

Rule one: When you have an iscoleles triangle (meaning that two sides are congruent), then the angles that the congruent sides make with the third side are congruent.

Rule two: Verticle angles are congruent. (Vertical angles are the angles on opposite sides of an intersection of line segments. For example, in the figure "X" the angles made by the "^" part and the "v" parts of the "X" are vertical angles. Likewise with the angles made by the "<" part and the ">" part.)

Rule three: All the angles in a triangle add up to 180 degrees.

So the first question could be solved by solving
4x-20=3x for x.

Answer 8

All of these problems have one thing in common. They involve isosceles triangles. An isosceles triange has two equal angles. The two sides opposite the two equal angles are equal in length.

1. Since the triangle is isosceles, the two indicated angles are equal.

4x - 20 = 3x.
x = 20°

2. x = 8°

3. x = 76°

4.

2*5x + 2x = 180°
12x = 180°
x = 15°

5.

4x + 2 = 6x - 30
32 = 2x
16° = x

6. x = 10°

Answer 9

see the arc on the angles? that means that they have the same measure.
The hash line on the sides means that they have the same length.

So, they are giving you equalities to solve:

1. 4x-20 = 3x
2. 3x-6 = x + 10
3. x + x + 28 = 180
4. 5x + 5x + 2x = 180
5. 6x-30 = 4x + 2
6. 3x + 10 = 5x - 10

Answer 10

your teacher should have been teaching about isosceles triangles.......anyway in your 1st figure as the sides are equal the angles opp to the equals sides are also equal thus,
4x-20=3x
so,x=20! for the 1st sum......