We have grown leaps and bounds to be the best Online Tuition Website in India with immensely talented Vedantu Master Teachers, from the most reputed institutions. Vedantu LIVE Online Master Classes is an incredibly personalized tutoring platform for you, while you are staying at your home. So, the required values of x and y are 42° and 88° respectively Y + 92° = 180° (interior angle + adjacent exterior angle = 180°.) X + 50° = 92° (sum of opposite interior angles = exterior angle) Solution: Using exterior angle property of triangle, Find the values of x and y in the following triangle. So, the three angles of the triangle are 40 0, 60 0 and 80 0 respectively.ģ. If the angles of a triangle are in the ratio 2:3:4, determine the three angles.īy interior angle sum property of triangle, So, the measure of the third angle of the given triangle is 75 0. Then,īy interior angle sum property of triangles, Solution: Let the third angle be ∠A and the ∠B = 60 0 and ∠C = 45 0. Two angles of a triangle are of measure 60 0 and 45 0.

Triangle ABC is such that, ∠A = 38° and ∠B = 134°. Let’s take a look at a few example problems: To find the third unknown angle of a triangle, subtract the sum of the two known angles from 180 degrees. When two interior angles of a triangle are known, it is possible to determine the third angle using the Triangle Angle Sum Theorem. It is also frequently used to calculate the exterior angles of a triangle when interior angles are given. This property is useful in calculating the missing angle in a triangle or to verify whether the given shape is a triangle or not. This means that the sum of all the interior angles of a triangle is equal to 180°. The angle sum property of triangles is 180°. Length of sides as an equilateral triangle, isosceles triangle and scalene triangle.Ī common property of all kinds of triangles is the angle sum property. Interior angles as an acute-angled triangle, obtuse-angled triangle and right-angled triangle. It has three interior angles on each of its vertices. The angle opposite to the longer side is larger and vice-versa.Ī triangle is the smallest polygon. In the right-angled triangle, the sum of two acute angles is 90°. The angles opposite to equal sides of an isosceles triangle are equal.Ī triangle can not have more than one right angle or more than one obtuse angle. Thus, the exterior angle of a triangle is equal to the sum of its opposite interior angles.įollowing are some important points related to angles of a triangle:Įach angle of an equilateral triangle is 60°. Proof: ∠3 and ∠4 form a linear pair because they represent the adjacent angles on a straight line.Īlso, from the interior angle sum property of triangle, it follows from the above triangle that:įrom equation (2) and (3) it follows that: Given: Consider a triangle ABC whose side BC is extended D, to form exterior angle ∠ACD. Theorem: If any one side of a triangle is produced then the exterior angle so formed is equal to the sum of two interior opposite angles. Thus, the sum of the interior angles of a triangle is 180°. Substituting the value of ∠3 and ∠1 in equation (1), Therefore, ∠3 = ∠ACB (a pair of alternate angles)Īlso, ∠1 = ∠ABC (a pair of alternate angles) Since, PQ || BC and AB, AC are transversals Proof: Since PQ is a straight line, From linear pair it can be concluded that: Theorem: The sum of interior angles of a triangle is 180° or two right angles (2x 90° )Ĭonstruction: Draw a line PQ parallel to side BC of the given triangle and passing through point A. In this article, we are going to learn the interior angle sum property and exterior angle property of a triangle. Angle sum property and exterior angle property are the two important attributes of a triangle. In a triangle, 3 sides and 3 angles are referred to as the elements of the triangle. A triangle with vertices A, B and C is denoted as ∆ABC. Triangle is the smallest polygon which has three sides and three interior angles, consisting of 3 edges and 3 vertices.

Triangle angle sum