Estimating Angles
Estimate and compare acute, obtuse, and reflex angles in degrees; classify angles by type and order them by size
What a learner can do afterwards
- Estimate an angle as approximately 130° and classify it as obtuse
- Identify a reflex angle in a diagram and estimate it as about 270°
- Order four angles from smallest to largest by estimation before measuring
1 · Read
You already know a full turn is 360 degrees and a quarter turn is 90 degrees. Estimating an angle means looking at it and guessing its size in degrees, before you check with a protractor. The best trick is to compare the angle to a right angle, which is exactly 90 degrees.
Angles have names based on their size. An acute angle is smaller than 90 degrees, like a narrow wedge. An obtuse angle is bigger than 90 degrees but smaller than 180 degrees, like a door opened wide. A reflex angle is bigger than 180 degrees, more than half of a full turn.
Priya looks at an angle that seems a bit wider than a right angle, maybe by a third again. She guesses about 130 degrees and calls it obtuse, since it's more than 90 degrees but less than 180. When she checks with a protractor, it reads 128 degrees. Her guess was close.
To order angles from smallest to largest without measuring, sort by type first: acute angles come before obtuse angles, and reflex angles always come last, since they pass the halfway point of a full turn.
Compare each angle to a right angle: acute is under 90 degrees, obtuse is between 90 and 180, and reflex is over 180.
More to read
Angle types review
Angles come in families by size. Acute angles are smaller than 90 degrees, right angles are exactly 90, obtuse angles sit between 90 and 180, and reflex angles stretch past 180 all the way to 360. Guess first, then measure. An angle clearly wider than a square corner but not flat is probably obtuse, near 120 or 130 degrees. A huge angle wrapping most of the circle is reflex, often near 270.
Angle basics review
Benchmarks make estimates honest. Compare any angle to 90, 180, and 270 degrees. Near 90 means acute or just obtuse, near 180 means almost straight, near 270 means three quarters round. Order angles without measuring by lining up one arm of each. The arm that opens widest belongs to the biggest angle. Sort smallest to largest before touching the protractor.
Reasoning about angles (part 1)
Reflex angles hide because people read the small side. The small side of a 270 degree angle is only 90 degrees. Always ask which side the angle opens before estimating. Subtract to check: 360 minus the small side gives the reflex side. If the small side is 90, the reflex side is 270. The two sides always add to a full turn.
Explore more
2 · Watch
به انگلیسیTake it off screen
Where it sits
Learn first
This opens up
Nothing builds on it yet.
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.