![]() ![]() ![]() These two angles (140° and 40°) are Supplementary Angles, because they add up to 180°: Notice that together they make a straight angle. Most notably, results in analysis involving trigonometric functions can be elegantly stated, when the functions' arguments are expressed in radians. Two Angles are Supplementary when they add up to 180 degrees. This is because radians have a mathematical "naturalness" that leads to a more elegant formulation of a number of important results. In calculus and most other branches of mathematics beyond practical geometry, angles are universally measured in radians. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right. angles are equal, then they are right angles. If the sum of two angles is 180 degrees then they are said to be supplementary angles, which form a linear angle together. Answer and Explanation: The supplementary angle of 80 is 100. ![]() All the large polygons in this diagram are regular polygons. Supplementary angles and complementary angles are defined with respect to the addition of two angles. Using the complementary angles formula, Supplementary Angle (X) 180° angle Supplementary Angle (X) 180° 105° Supplementary Angle (X) 75° The value of angle X is 75°. The relation 2 π rad = 360° can be derived using the formula for arc length, ℓ arc = 2 π r ( θ 360 ∘ ) Usage Mathematics We all know that the supplementary angles add up to 180°, so subtract 105° from 180° to find the supplement angle. Properties Used in Angle Chasing Two angles that are complementary add to Vertical angles are congruent to each other. Thus 2 π radians is equal to 360 degrees, meaning that one radian is equal to 180/ π degrees ≈ 57.29577 95130 82320 876. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted so long as the latter page exists. The magnitude in radians of one complete revolution (360 degrees) is the length of the entire circumference divided by the radius, or 2 π r / r, or 2 π. Text and/or other creative content from this version of Supplementary angles was copied or moved into Angle with this edit on 04:43, 20 November 2013. More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle that is, θ = s/ r, where θ is the subtended angle in radians, s is arc length, and r is radius. One radian is defined as the angle subtended from the center of a circle which intercepts an arc equal in length to the radius of the circle. ![]()
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