![]() A triangle is the smallest polygon having three sides and three interior angles, one at each vertex, bounded by a pair of adjacent sides. ![]() In a Euclidean space, the sum of the measure of the interior angles of a triangle sum up to 180 degrees, be it an acute, obtuse, or a right triangle which is the direct result of the triangle sum theorem, also known as the angle sum theorem of the triangle. Triangle ADB and BDC are isosceles triangles.The triangle sum theorem states that the sum of all the interior angles of a triangle is 180 degrees. Therefore, the angles of the triangle are 30°, 50°, and 100°.įind the missing angles in the diagram below. Hence, the missing angles are 60° and 55°Ĭalculate the value of x for a triangle whose angles are x°, (x + 20) ° and (2x + 40) °. Solve the two simultaneous equations by substitution Therefore, the three angles of a triangle are 33°, 48° and 81°.įind the missing interior angles of the following diagram.Īngle y ° and (2x + 10) ° are supplementary angles (sum is 180°) This is an isosceles right triangle therefore, one angle is 90°įind the angles of a triangle whose second angle exceeds the first angle by 15° and the third angle is 66° more than the second angle. Calculate ∠C.įind the missing angles x in the triangle shown below.īy Triangle Angle Sum Theorem (Sum of interior angles = 180°)įind the missing angles inside the triangle below. ![]() 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. How to Find the Interior Angles of a Triangle? This now brings us to an important theorem in geometry known as Triangle Angle Sum Theorem.Īccording to the Triangle Angle Sum Theorem, the sum of the three interior angles in a triangle is always 180°. One common property about triangles is that all three interior angles add up to 180 degrees.
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