Lets find the sizes of unknown amgles?

To find the sizes of unknown angles, we can use the properties of angles in different geometric shapes such as triangles, quadrilaterals, and circles.

1. In a triangle, the sum of the angles is always 180 degrees. So, if we know the measures of two angles in a triangle, we can find the measure of the third angle by subtracting the sum of the known angles from 180 degrees.

2. In a quadrilateral, the sum of the angles is always 360 degrees. So, if we know the measures of three angles in a quadrilateral, we can find the measure of the fourth angle by subtracting the sum of the known angles from 360 degrees.

3. In a circle, the angle at the center of a circle is twice the angle at the circumference that subtends the same arc. So, if we know the measure of an angle at the center of a circle, we can find the measure of the angle at the circumference by dividing the center angle by 2.

These are just a few examples of how we can find the sizes of unknown angles using geometric properties. There are many other properties and theorems that can be used depending on the specific shape and situation.

1. Finding the Size of an Angle in a Triangle

If the sum of the interior angles of a triangle is 180 degrees, we can use this to find the size of an unknown angle.

For example, in a triangle with angles x, y, and z:

```
x + y + z = 180 degrees
```

If we know the size of two angles, we can find the size of the third angle by subtracting the known angles from 180 degrees.

2. Finding the Size of an Angle in a Parallelogram

In a parallelogram, opposite angles are equal. So, if we know the size of one angle, we know the size of the opposite angle.

3. Finding the Size of an Angle in a Rectangle

In a rectangle, all four angles are right angles (90 degrees).

4. Finding the Size of an Angle in a Circle

The circumference of a circle is divided into 360 degrees. So, if we know the fraction of the circumference represented by an angle, we can find the size of the angle.

For example, if an angle represents 1/4 of the circumference of a circle, then the angle is:

```
1/4 - 360 degrees = 90 degrees
```

5. Finding the Size of an Angle in a Regular Polygon

In a regular polygon with n sides, the sum of the interior angles is:

```
(n - 2) - 180 degrees
```

So, to find the size of one interior angle, we divide this sum by the number of sides:

```
Angle = (n - 2) - 180 degrees / n
```

For example, in a regular hexagon with 6 sides:

```
Angle = (6 - 2) - 180 degrees / 6 = 120 degrees
```