![]() X + x + 35 = 180 (Sum of the interior angles of a triangle is equal to 180°). The two base angles of an isosceles triangle are equal, so we can assume each as x. Angles opposite to the equal angles are also equal. The Exterior Angle theorem states that measure of an exterior angle of a triangle is equal to the sum of two non-adjacent interior angles.įind the measure of an exterior angle at the base of an isosceles triangle whose vertex angle measures 35°.Īs we know that the two sides of an isosceles triangle are equal. If the two non-adjacent interior angles are represented by 2x + 8, and 4x – 17, find the value of x. In Triangle ABC, an exterior angle at D is represented by 5x + 11. Measure of exterior angle adjacent to angle C = m∠A + m∠B = 60° + 45° = 105°. Measure of exterior angle adjacent to angle B = m∠A + m∠C = 60° + 75° = 135°. We know that the sum of the interior angles of a triangle = 180°. To find the measure of other exterior angles Measure of exterior angle adjacent to angle A = m∠B + m∠C = 45° + 75° = 120°. In the triangle given below, external angles and internal angles are shown.Įxterior Angle Theorem Examples How to find exterior angles Example 1 The exterior angles of a triangle are the angles that form an adjacent pair with the interior angles by extending the sides of the triangle. External theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles (opposite interior angles).Įxterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the two opposite interior angles. With the help of exterior angle theorem, unknown interior and exterior angles of a triangle can be found easily.Īs shown in the figure above, interior angles of the triangle are angle 1, angle 2 and angle 3.Īngle 4 is the exterior angle adjacent to the angle 3.Īngle 1 and angle 2 are the opposite interior angles (remote interior angles) to the exterior angle 4. ImportanceĮxterior angle theorem is one of the important theorems of the triangle. Exterior angle is always supplementary to its adjacent interior angle.Įxterior angle theorem could be used to find the measures of the unknown interior and exterior angles of a triangle.Exterior angle is always greater than the either of the two remote interior angles.Exterior angle is always equal to the sum of the opposite interior angles.The exterior angle is not just outside the triangle but it is also adjacent to an interior angle.Įxterior angle theorem also states that the measure of an exterior angle of a triangle is greater than either of the two opposite interior angles (remote interior angles).Īlternate Exterior Angles Theorem Characteristics Definition: Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two non-adjacent interior angles (opposite interior angles).Īn exterior angle of a triangle is formed by the extension of any one side of the triangle.
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