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Pedagogical Angle Practice & Estimation Loop

Angle Practice Studio.

Estimate angles, test geometric relationships, and reveal answers. Toggle a virtual protractor to practice manual reading.

Paper Style:
📱 Drag ray to set angle • Scroll page outside canvas
Estimate & Verify

Single Angle Practice

Estimate the angle type and magnitude, then click to reveal answers.

Key Geometric Rules
How to Practice
📐 Angle Reference

Types of Angles & Relationships

A quick reference for angle classifications, ranges, and geometric properties.

0° < θ < 90°Acute

Acute Angle

An angle strictly between 0° and 90°. Common examples include roof pitches, equilateral triangle corners (60°), and scissor blades.

Trig: sin(θ) > 0, cos(θ) > 0
θ = 90°90° Square

Right Angle

An angle of exactly 90° (π/2 radians), forming perpendicular lines found in door frames, books, and square corners.

Trig: sin(90°) = 1.0, cos(90°) = 0
90° < θ < 180°Obtuse

Obtuse Angle

An angle greater than 90° but less than 180°. Found in reclined seats, wide roof gables, and hockey stick shafts.

Trig: sin(θ) > 0, cos(θ) < 0
θ = 180°180° Flat

Straight Angle

An angle of exactly 180° (π radians). The two arms point in opposite directions to form a continuous straight line.

Trig: sin(180°) = 0, cos(180°) = -1.0
180° < θ < 360°Reflex

Reflex Angle

An angle strictly greater than 180° and less than 360°. Represents the major outer arc measured by a 360° full-circle protractor.

Outer Arc = 360° − Inner Angle
θ = 360° (2π rad)Full Circle

Complete Angle (360°)

A full 360° rotation where the ray circles completely back to the baseline (equal to 1 full turn or 2π radians).

Trig: sin(360°) = 0, cos(360°) = 1.0
Sum = 90° or 180°Pairs

Angle Pairs

• Complementary: Two angles that add up to 90°.
• Supplementary: Two angles that add up to 180°.

Opposite Angles: Equal (a = c)
Sum = 360° | 4 QuadrantsExplementary

Conjugate Angles

Two angles that add up to 360° (a + b = 360°). Divided into four 90° quadrants: Q I (0–90°), Q II (90–180°), Q III (180–270°), and Q IV (270–360°).

Bearings: Clockwise from North