An angle is formed when two rays or lines meet at a common endpoint. The common endpoint is called the vertex of the angle. Angles are measured in degrees, and understanding angles is an important concept in geometry.

There are several types of angles that you should be familiar with:

**Acute Angle:**An angle that measures between 0 and 90 degrees.**Right Angle:**An angle that measures exactly 90 degrees.**Obtuse Angle:**An angle that measures between 90 and 180 degrees.**Straight Angle:**An angle that measures exactly 180 degrees.**Reflex Angle:**An angle that measures between 180 and 360 degrees.

There are several important angle relationships to understand:

**Vertical Angles:**When two lines intersect, the angles opposite each other are called vertical angles and are congruent (have the same measure).**Adjacent Angles:**Two angles are adjacent if they have a common vertex and a common side, but do not overlap.**Complementary Angles:**Two angles are complementary if the sum of their measures is 90 degrees.**Supplementary Angles:**Two angles are supplementary if the sum of their measures is 180 degrees.

Angles are measured in degrees using a protractor. When measuring angles, the protractor is placed so that the vertex is at the center of the protractor, and one side of the angle aligns with the zero line. The measure is then read where the other side of the angle intersects the protractor.

It's important to understand the properties of angles, such as the fact that the sum of the interior angles of a triangle is always 180 degrees, and the sum of the interior angles of a quadrilateral is always 360 degrees.

When studying angles, make sure to:

- Memorize the types of angles and their respective measures.
- Practice identifying and measuring angles using a protractor.
- Understand the relationships between angles, such as vertical angles, adjacent angles, complementary angles, and supplementary angles.
- Practice solving problems involving angle properties, such as finding missing angles in geometric figures.

Understanding angles is fundamental in geometry and will help you solve various problems involving shapes and spatial reasoning. Good luck with your studies!

.Study GuideMeasurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference

Geometry (NCTM)

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

Connections to the Grade 7 Focal Points (NCTM)

Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.