Respuesta :
If one of the outer corners of an isosceles triangle is 115 degrees, then the internal angle is 180-115 = 65 degrees.
The task has 2 solutions.
Let the angle at the vertex is 65 degrees. Then the angles at the base are (180-65): 2 = 57.5 degrees.
Let the angle at the base be 65 degrees, then another angle at the base is 60 degrees. The vertex angle is 180- (65 + 65) = 50 degrees.
Answer:
Case 1: The measure of interior angles are : 65°, 57.5°, 57.5°
Case 2: The measure of interior angles are : 65°, 65°, 50°
Explanation:
We are given an isosceles triangle. In the triangle two sides and two angles having the same measures.
We are given an exterior angle 115°.
So the corresponding interior angle is 180-115 = 65 degrees.
We need to find other two interior angles.
Case 1:
If the given exterior angle is top of the vertex angle, then the base of the interior angles are:
(180-65) ÷ 2 = 57.5°. {because in isosceles triangle two sides and two angles having the same measures]
So, each base angles measures 57.5°.
The measure of interior angles are : 65°, 57.5°, 57.5°
Case 2:
If the given measure of exterior angle is in base, then one angle must be 65°.
Other angle = (180 - (65 +65)) = 180 - 130 = 50°
The measure of interior angles are : 65°, 65°, 50°
