Mathematics Grade 7 15 min

Angles of 90, 180, 270, and 360 degrees

Angles of 90, 180, 270, and 360 degrees

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Introduction & Learning Objectives

Learning Objectives Identify and define angles of 90, 180, 270, and 360 degrees. Classify these specific angles based on their measure. Draw angles of 90, 180, 270, and 360 degrees using a protractor or visual estimation. Relate these angles to fractions of a full turn or rotation. Solve simple problems involving turns and rotations using these specific angle measures. Recognize real-world examples of 90, 180, 270, and 360-degree angles. Have you ever wondered how much a skateboarder spins in a '360' trick, or how far a clock's hand moves in half an hour? ⏰ These are all about special angles! In this lesson, we'll explore four fundamental angle measures: 90, 180, 270, and 360 degrees. Understanding these specific angles is crucial for grasping more comp...
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Key Concepts & Vocabulary

TermDefinitionExample Degree ($\text{°}$)A unit of measurement for angles, representing $\frac{1}{360}$ of a full circle.A small turn might be 10 degrees, while a larger turn could be 90 degrees. Right AngleAn angle that measures exactly 90 degrees. It forms a perfect 'L' shape and is often marked with a small square symbol.The corner of a square table or the angle where a wall meets the floor. Straight AngleAn angle that measures exactly 180 degrees. It forms a straight line.Looking straight ahead, then turning to look directly behind you represents a 180-degree turn. Reflex Angle (270 degrees)An angle that measures greater than 180 degrees but less than 360 degrees. 270 degrees is a specific type of reflex angle.If you start facing North and turn clockwise to face West, you&#0...
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Core Formulas

Angle-Turn Equivalence Rule A $\frac{1}{4}$ turn is $90^{\circ}$, a $\frac{1}{2}$ turn is $180^{\circ}$, a $\frac{3}{4}$ turn is $270^{\circ}$, and a full turn is $360^{\circ}$. This rule helps relate fractions of a circle or rotation to their corresponding angle measures. It's fundamental for understanding movement and orientation. Angles on a Straight Line Rule Angles that form a straight line (or a straight angle) sum up to $180^{\circ}$. If you have multiple angles adjacent to each other that together form a straight line, their measures will always add up to 180 degrees. This is useful for finding unknown angles. Angles Around a Point Rule The sum of angles around a central point (a full rotation) is $360^{\circ}$. When several angles share a common vertex...

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Sample Practice Questions

Challenging
A person is facing South. They make a 180° turn, and then a 270° turn clockwise. What is their final direction?
A.North
B.West
C.East
D.South
Challenging
In a diagram, an angle is marked with the small square symbol, indicating it is 90°. What is the measure of the corresponding reflex angle around the same vertex?
A.270°
B.180°
C.90°
D.360°
Challenging
A circular pizza is cut into 4 equal slices. If you remove 3 of the slices, what is the measure of the reflex angle formed by the empty space at the center of the pizza?
A.90°
B.180°
C.270°
D.360°

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