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How to Find the Value of x in a Triangle?

TopBefore discussing on how to find the value of x in a triangle? let’s discuss about triangle. A closed figure bounded by three boundaries or line segments is called a triangle. Based on the sides and the angle between these sides, the triangle can be categorized into four types namely:
1. Equilateral Triangle: All the angles are equal and measure 60°
2. Scalene Triangle: A triangle is said to be scalene if all the sides are unequal i.e. they have different measurements.
3. Isosceles Triangle: A triangle is said to be isosceles when two of its sides are equal (also the angles opposite to these sides will be equal too).
4. Right – Angle Triangle: One angle is Right Angle or 90°and the side opposite to it is called the hypotenuse (considered to be the longest side in the triangle).
Following the properties of the above mentioned Triangles we can solve the value of ‘x’.
For example consider the following triangle:


As the triangle given has two sides equal i.e.
AB = BC,
So, ÐABC = ÐACB or y = 60°
Solving for x: As we know that the sum of all the angles of a triangle is equal to 180°,
So, ÐABC + ÐACB + ÐBAC = 180,
x + y + 60 = 180
Substituting the value of y in the above equation we get,
x + 60 + 60 = 180,
Or x = 180 – 120,
Or x = 60.
Thus the resulting triangle is an Equilateral Triangle with all its angles 60°.
Next we consider an example of how to find the value of x in a triangle with sides given:


In the triangle PQR we have considered that all the angles are equal. So,
ÐRPQ = ÐPRQ = ÐPQR,
This implies: PR = PQ and RQ = PQ,
OR 3x = 54 and 6y = 54,
Or x = 18 and y = 9. Hence, Solved