Exterior Angles Of A Triangle Video Lessons Examples Step By Step Example 2: if one interior angle of a triangle is 56°, find the measure of its corresponding exterior angle. solution: according to the properties of the exterior angle of a triangle, each interior angle forms a linear pair with its respective exterior angle. Exterior angle theorem. the exterior angle d of a triangle: equals the angles a plus b. is greater than angle a, and. is greater than angle b. example: the exterior angle is 35° 62° = 97°. and 97° > 35°. and 97° > 62°.
Exterior Angle Formula Concept And Solved Examples An exterior angle of a triangle is equal to the sum of the two opposite interior angles, thus an exterior angle is greater than any of its two opposite interior angles; for example, in Δabc, ∠5 = ∠a ∠b. the sum of an exterior angle and its adjacent interior angle is equal to 180 degrees; for example, ∠5 ∠c = 180°. The above statement can be explained using the figure provided as: according to the exterior angle property of a triangle theorem, the sum of measures of ∠abc and ∠cab would be equal to the exterior angle ∠acd. general proof of this theorem is explained below: proof: consider a ∆abc as shown in fig. 2, such that the side bc of ∆abc is. Example 1: find the values of x and y by using the exterior angle theorem of a triangle. solution: ∠x is the exterior angle. ∠x 92 = 180º (linear pair of angles) ∠x = 180 92 = 88º. applying the exterior angle theorem, we get, ∠y 41 = 88. ∠y = 88 41 = 47º. therefore, the values of x and y are 88º and 47º respectively. An exterior angle of a triangle is equal to the sum of the two opposite interior angles. example: find the values of x and y in the following triangle. solution: x 50° = 92° (sum of opposite interior angles = exterior angle) x = 92° – 50° = 42°. y 92° = 180° (interior angle adjacent exterior angle = 180°.) y = 180° – 92° = 88°.
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