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If you have a protractor or an angle-finder tool, you can use that to check the angle. To deduce angles using mathematics, we use the trigonometric functions sine, cosine and tangent, basic triangular geometry and some algebra.
The 180 degree rule of triangles
In any given triangle, all three angles must add up to 180 degrees. Thus if we know any two of the angles, we can deduce the third by subtracting the sum of those two angles from 180.
If we only know one of the angles, then we need to know the lengths of at least two sides to determine the other angles.
Labelling triangles
It is useful to label triangles in a standard fashion. We normally label the three sides using lower case, a, band c. The angles opposite these sides are labelled in upper case, A, B and C, such that angle A is opposite side a and angle B is opposite side b.
Sine rule
The sine rule is used whenever we know the lengths of any two sides and at least one opposing angle, or we know two angles and at least one opposing side. The sine rule states that:
a/sin(A) = b/sin(B) = c/sin(C)
Cosine rule
The cosine rule is used when we know at least two sides and only one angle, where the known angle is not opposite a known side. The cosine rule states that:
cos(A) = (b2 + c2 - a2) / 2bc
Thus we can determine the length of the third side using:
a2 = b2 + c2 - 2bc cos(A)
Knowing all three sides allows us to determine either of the remaining angles using the sine rule followed by the 180 rule to determine the final angle.
Right-angled triangles and Pythagoras' theorem
A right-angled triangle is any triangle where one of the angles is exactly 90 degrees. In order to discover the other two angles we must know the lengths of at least two sides. The side opposite the right-angle is always known as the hypotenuse (and is always the longest side).
Pythagoras' Theorem tells us that, for any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Thus for any right-angled triangle where a is the hypotenuse:
a2 = b2 + c2
Knowing all three sides allows us to determine the two missing angles using the sine rule. However, in right angled triangles, we can use a simpler method. If we want to discover the angle of B, where a is the hypotenuse, then c becomes the adjacent side and b is the opposite side. Thus any of the following can be used to determine the angle of B:
sin(B) = opposite/hypotenuse
cos(B) = adjacent/hypotenuse
tan(B) = opposite/adjacent
In other words, where angle A is 90 degrees:
sin(B) = b/a
cos(B) = c/a
tan(B) = b/c
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What is an angle measuring between 91 degrees and 179 degrees?
It is an "obtuse angle."Angles that are less than 90 degrees are "acute angles."Angles that are exactly 180 degrees are "straight angles."Angles that are exactly 90 degrees are "right angles."
Angles two angles who's sum is 180 degrees?
Angles that add to 180 degrees are called supplementary angles, while angles that add to 90 degrees are called complentary angles.
What angles Does the decagon have?
The internal angles are 144 degrees. The external angles are 36 degrees.
How can you find the sum of the exterior angles in any polygon?
The exterior angles of any polygon add up to 360 degrees
Can you make a supplementary angle out of 3 angles?
you can use up to 2 angles in a supplementary angle. Just find 2 angles to fit into 180 degrees.
How do you find the angle degrees?
A protractor is nused to measure angles in degrees.
How do you find the number of degrees in a decagon?
The sum of the interior angles is 1440 degrees.
How do you find angles?
Supplementary angles add up to 180 degrees on a straight line
If two angles are supplementary angles and one angle is 30 degree less than twice the other find the angles?
The angles could be 105 degrees and 75 degrees because they both add up to 180 degrees
What is the formula to find the exterior angles?
The sum of the exterior angles of any polygon is 360 degrees.
How do you find the missing angle of a square with no given angles?
All the angles of a square are 90 degrees.
Can you find the reference angle of a quadrantal angle?
Yes. Quadrantal angles have reference angles of either 0 degrees (e.g. 0 degrees and 180 degrees) or 90 degrees (e.g. 90 degrees and 270 degrees).
How do you find angles on an isosceles trapezoid?
Use a protractor and you'll find base angles are equal and that the 4 interior angles add up to 360 degrees
What is the angle of a triangle measuring 68 X 68 X 82?
It is an isosceles triangle having 3 interior angles 2 of which are equal in size and the 3 angles add up to 180 degrees. Use Pythagoras' theorem to find its altitude and then use trigonometry to find the sizes of its angles. The angles work out as 53 degrees, 53 degrees and 74 degrees
What are the angles of a triangle that has sides of 123 cm 97 cm and 79 cm?
Let the angles be A B C and their opposite sides be a b c and use the cosine rule to find the first two angles and then deduct them from 180 degrees to find the third angle and so therefore it follows that the angles are: 88.05 degrees, 52.01 degrees and 39.94 degrees.
What is the third angle of a triangle if two of them are 45 degrees and 110 degrees?
To find the third angle of a triangle when two angles are known, you can use the fact that the sum of all three angles in a triangle is always 180 degrees. Therefore, if two angles are 45 degrees and 110 degrees, you can add these together to find the sum of the two known angles (45 + 110 = 155 degrees). Then, subtract this sum from 180 degrees to find the measure of the third angle: 180 - 155 = 25 degrees. Thus, the third angle of the triangle is 25 degrees.
What is supplementary angles in geometry?
Supplementary angles are any angles in which their degrees add to a sum of 180o. In the related links you will find an example of Supplementary angles.
