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  2. Acute and obtuse triangles - Wikipedia

    en.wikipedia.org/wiki/Acute_and_obtuse_triangles

    An obtuse triangle (or obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90°) and two acute angles. Since a triangle's angles must sum to 180° in Euclidean geometry , no Euclidean triangle can have more than one obtuse angle.

  3. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    An angle larger than a right angle and smaller than a straight angle (between 90° and 180°) is called an obtuse angle [6] ("obtuse" meaning "blunt"). An angle equal to ⁠ 1 / 2 ⁠ turn (180° or π radians) is called a straight angle. [5] An angle larger than a straight angle but less than 1 turn (between 180° and 360°) is called a reflex ...

  4. Law of cosines - Wikipedia

    en.wikipedia.org/wiki/Law_of_cosines

    Fig. 7a – Proof of the law of cosines for acute angle γ by "cutting and pasting". Fig. 7b – Proof of the law of cosines for obtuse angle γ by "cutting and pasting". One can also prove the law of cosines by calculating areas. The change of sign as the angle γ becomes obtuse makes a case distinction necessary. Recall that

  5. Trapezoid - Wikipedia

    en.wikipedia.org/wiki/Trapezoid

    An acute trapezoid has two adjacent acute angles on its longer base edge. An obtuse trapezoid on the other hand has one acute and one obtuse angle on each base. An isosceles trapezoid is a trapezoid where the base angles have the same measure. As a consequence the two legs are also of equal length and it has reflection symmetry. This is ...

  6. Non-Euclidean geometry - Wikipedia

    en.wikipedia.org/wiki/Non-Euclidean_geometry

    The summit angles of a Saccheri quadrilateral are acute if the geometry is hyperbolic, right angles if the geometry is Euclidean and obtuse angles if the geometry is elliptic. The sum of the measures of the angles of any triangle is less than 180° if the geometry is hyperbolic, equal to 180° if the geometry is Euclidean, and greater than 180 ...

  7. Euclidean geometry - Wikipedia

    en.wikipedia.org/wiki/Euclidean_geometry

    The sum of the angles of a triangle is equal to a straight angle (180 degrees). [14] This causes an equilateral triangle to have three interior angles of 60 degrees. Also, it causes every triangle to have at least two acute angles and up to one obtuse or right angle.

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  9. Isosceles trapezoid - Wikipedia

    en.wikipedia.org/wiki/Isosceles_trapezoid

    In the picture below, angles ∠ABC and ∠DCB are obtuse angles of the same measure, while angles ∠BAD and ∠CDA are acute angles, also of the same measure. Since the lines AD and BC are parallel, angles adjacent to opposite bases are supplementary, that is, angles ∠ABC + ∠BAD = 180°.