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How Many Degrees in a Triangle?

TopTriangle is made of three arms (or three line segments or three edges) and three angles (shapes). Triangle is the basic shape of Geometry. Various types of Triangles are Equilateral Triangle, isosceles triangle, scalene triangle, right triangle (or right-angled or Rectangle triangle), oblique triangles, acute triangle (or acute-angled triangle), obtuse triangle (or obtuse-angled triangle) etc. Internal angles of any type of triangle sum up to 180°. In other words, we can say that a triangle has three angles and addition of angles equals to 180° or π / 2 radians. Let’s consider a triangle with vertices (edges) P, Q, and R.

This triangle will be denoted as ∆PQR. Here p, q and r denote three angles of triangle. This triangle is formed by three line segments which are PQ, QR and RP. P, Q and R are vertices of triangle. Vertices are also called edges of triangle. For any triangle it is universal truth that addition of all three angles will be one eighty degree (1800). Mathematically, it can be expressed as:
∠p + ∠q + ∠r = 180°,
If we are given two angles out of three then substituting these values, one angle can be calculated using above formula.
If for a triangle p = 75° and q = 85° then angle ∠r = ?,
Since we know that for any triangle ∠p + ∠q + ∠r = 180°,
75° + 85° + ∠r = 180°,
Then ∠r = 180° - 160° = 20°,
Lets prove that how many degrees in a triangle are there.
In following triangle angles add up to one eighty degree.


∠x + ∠y + ∠z = 180°
The line at the top (that touches the top of the triangle) is parallel to the base line of triangle. Hence angles ‘x’ are same and also angles ‘y’ are same and it can be easily seen that x + y + z does a complete rotation from one side of Straight Line to other, or 180°.