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The formula for Finding Angles
Let's look at some examples of circumstances when we might need to use these formulas before understanding them. Depending on the facts supplied, multiple formulas for finding angles exist.
- The sum of interior angles formula is used to locate the missing angle in a polygon.
- We utilise trigonometric ratios to compute the missing angle in a right-angled triangle.
- We apply laws of sines and cosines to identify the missing angles in a non-right-angled triangle.
What Is the Angle Finding Formula?
The formulas for finding angles are listed below. Using the available information, we choose one of these formulas to find the unknown angles.
| Formula Name | Formula | How to find unknown angles? |
|---|---|---|
| In a polygon with n sides, the sum of interior angles | 180 (n-2) degrees | Using this formula, get the sum of all interior angles and subtract the total of all known angles to get the unknown interior angle. |
| sin, cos, and tan | opposite / hypotenuse = sin θ cosθ = adjacent / hypotenuse tanθ = opposite / adjacent cos | To find the unknown angle, use one of these trigonometric ratios, depending on which two sides are given. |
| Law of sines | a/sin A = b/sin B = c/sin C A, B, and C are the angles of a triangle, and a, b, and c are the opposing sides of the triangle. | When we have a) two sides and a non-included angle (or) b) two angles and a non-included side, we can apply the law of sines to find unknown angles. |
| Law of cosines | a2= b2+ c2- 2bc cos A b2= c2+ a2- 2ca cos B c2= a2+ b2- 2ab cos C The angles A, B, and C of a triangle are represented by a, b, and c, respectively. |
When we have a) three sides (or) b) two sides and the included angle, we utilise the law of cosines to find unknown angles. |
Example: Find the fifth interior angle of a pentagon if four of its interior angles are 108°, 120°, 143°, and 97°.
Sol: Number of sides of the pentagon, n = 5.
Sum of all 5 interior angles of pentagon = 180 (n -2)° = 180 (5 - 2)° = 540°.
Sum of the given 4 interior angles = 108°+ 120°+ 143°+ and 97°= 468°.
So fifth interior angle = 540° - 468° = 72°.
Download the pdf for Interior Angles
