Obtuse Angles

An obtuse angle is any angle larger than 90° and smaller than 180°: past a right angle, not yet flat. Obtuse angles cover the range between a right angle and a straight line. Common in everyday objects (an open laptop, a reclined beach chair, a door swung wide), less visually striking than acute or reflex angles.

Examples Across the Range

That gives 88 integer values to sort through, from 91° to 179°. Five useful reference points, drawn at a shared vertex:

120° is the most useful value to memorise. It is one-third of a full circle, and every interior angle of a regular hexagon: the same angle found in a honeycomb cell. 135° is the other handy landmark: a right angle plus 45°, roughly the angle of a flag at half-mast.

Obtuse Angles in Everyday Life

A reclined beach chair or sofa back.
An open book held nearly flat in the lap.
Every interior corner of a regular hexagon, exactly 120°.
Clock hands at 4 o'clock land on 120°.
The bend in a boomerang.
A door swung past 90° against its frame.

Obtuse Triangles

A triangle with one obtuse interior angle is an obtuse triangle. The arithmetic forces the other two corners to share whatever remains of 180°, which is not much. A 120° angle in one corner leaves only 60° for the other two to split.

A second obtuse angle cannot fit. Two obtuse values alone already exceed 180°. The same reasoning rules out the obtuse-plus-right-angle case. Every triangle gets at most one obtuse corner.

Supplements

Two angles are supplementary when they sum to 180°. An obtuse angle always pairs with an acute one. Common pairs:

120° and 60°
135° and 45°“, ”150° and 30°“, ”100° and 80°

Wherever two lines cross, the four resulting angles pair off into two supplementary sets. The same arrangement appears at every corner of a parallelogram.

Practise Spotting Obtuse Angles

Roughly a quarter of daily Angledle puzzles sit in obtuse territory. The hard part is telling 100° from 130° from 160° on sight. A reliable anchor is 135°: a right angle tipped halfway over. Once that value reads cleanly, the others sort themselves out. For more reps, see Unlimited mode.

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