Is exactly 180° a reflex angle?

Exactly 180° is a straight angle. A reflex angle must exceed 180° and remain below 360°, so this tool excludes both boundaries.

Can an obtuse opening have a reflex counterpart?

An obtuse opening between 90° and 180° leaves a larger region between 180° and 270°. For example, 150° corresponds to a 210° reflex angle.

Does rotating the whole diagram change the reflex value?

Moving both rays by the same rotation preserves their separation. The smaller and larger regions remain the same sizes even when neither ray is horizontal.

Reflex Angle Calculator

The reflex angle calculator finds the larger angle formed by two rays when the smaller region is known, or recovers the smaller region from a known reflex angle. Both regions share the same vertex and together complete one 360° turn. A reflex angle is strictly greater than 180° and strictly less than 360°. The circular diagram marks both arcs so you can see which region the answer describes.

Identify the larger region with the reflex angle calculator

Two rays usually enclose a short route and a long route around their vertex. Measuring only the smaller opening can miss the region requested by a reflex-angle question. Look for an arc drawn outside the smaller gap or an explicit instruction to find the angle greater than a half turn. The result is a size, not a clockwise or counterclockwise sign convention, and the same pair of rays supports both regions.

Use either side of the full-turn relationship

Select Smaller → Reflex when the known angle is the smaller opening. Enter a degree value strictly between 0° and 180°. Acute, right, and obtuse inputs all have valid reflex counterparts.
Select Reflex → Smaller when the known region is already larger than a straight angle. Enter a value strictly between 180° and 360°. The smaller answer must lie strictly between zero and a half turn.
Read the equation 360° minus your input and compare the two arc labels. The interface shows the smaller angle's type, the reflex classification, and both radian values without asking you to switch tools.
Use Calculate by mouse, touch, or keyboard after editing. Results also update directly with valid input. Reset returns to the selected mode's example so you can compare a familiar opening with its larger counterpart.

Why subtract from 360 degrees?

The two nonoverlapping regions between the same rays partition a complete turn. Therefore smaller + reflex = 360°, reflex = 360° − smaller, and smaller = 360° − reflex. The operation is its own inverse.
The open endpoints matter. An input of 180° leaves another 180° straight angle, not a reflex angle. Zero would leave a full 360° turn, and 360° would leave zero. These boundary values are excluded rather than labeled reflex by rounding or convention.
Radians describe the same region in another unit: radians = degrees × π / 180. The two radian outputs sum to 2π, just as the degree outputs sum to 360. Decimal radians are approximate displays of the internal calculation.
The smaller region is acute below 90°, right at 90°, and obtuse above 90° but below 180°. Its counterpart remains reflex across that entire domain. Angle type describes the size of the region, not the apparent slope of either individual ray.

Worked reflex-angle examples

A smaller opening of 35° leaves reflex = 360° − 35° = 325°. The shorter arc is acute, while the long arc passes through most of the circle. Its radian size is approximately 5.672320.
A right angle of 90° has a 270° reflex counterpart. One arc occupies one quarter of a turn, and the other occupies three quarters. Their exact radian expressions are π/2 and 3π/2.
An obtuse opening of 145° leaves 215°. This example demonstrates that the smaller input need not be acute: it only needs to remain below 180°. Conversely, a given 240° reflex region leaves a 120° obtuse opening.
Students use the relationship when a worksheet marks the outside angle between rays. Illustrators can describe the long rotation in a circular motif. For drawing a chosen ray opening rather than calculating its counterpart, continue to Angle Maker and select the appropriate angle convention.

Reflex, supplementary, and full angles differ

Supplementary angles total 180°, so the supplementary counterpart of 35° is 145°. Its reflex counterpart is 325° because it completes a full turn. Complementary angles total 90° and answer another question again. A full angle is exactly 360°; it is not included in the reflex interval.

A signed rotation such as −120° indicates direction. Its final ray can coincide with a positive 240° rotation, but the negative value is not itself an unsigned reflex-angle size. Use the angle converter's normalization controls when the task is about equivalent directions or turns beyond one revolution.

Precision and reading the intended arc

The reflex angle calculator rejects empty, nonfinite, and out-of-domain values. Extremely close endpoints can become indistinguishable after floating-point subtraction; such inputs produce a precision message instead of an excluded 360° or 180° counterpart. Ordinary numeric displays use up to six decimal places, while extreme small values use six significant digits. Calculations retain the unrounded input. The drawing is a schematic aid, not an image measurement or calibrated instrument. Always identify the marked region before applying the formula, and do not subtract from 180° merely because a worksheet also contains straight lines.