Equilateral pentagon of δ can be seen from the figure: Simplifying, δ is obtained as function of α and β: The remaining angles of the pentagon can be found geometrically: The remaining angles of the orange and blue triangles are readily found by noting that two angles of an isosceles triangle are equal while all three angles sum to 180°. Then formula_7 and the two remaining angles of the green triangle can be found from four equations stating that the sum of the angles of the pentagon is 540°, the sum of the angles of the green triangle is 180°, the angle
Hyperbolic triangle side with the corresponding letter) is strictly less than a straight angle. The difference between the measure of a straight angle and the sum of the measures of a triangle's angles is called the defect of the triangle. The area of a hyperbolic triangle is equal to its defect multiplied by the square of : This theorem, first proven by Johann Heinrich Lambert, is related to Girard's theorem in spherical geometry. In all the formulas stated below the sides , , and must be measured in absolute length, a unit so that the Gaussian curvature of the plane is −1.