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Question
If the exterior angle of a triangle is 140° and its interior opposite angles are equal, find all the interior angles of the triangle
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Solution
Given the exterior angle = 140°
Interior opposite angle are equal
Let one of the interior opposite angle be x
Then x + x = 140° ..........[∵ Exterior angle = sum of interior opposite angles]
2x = 140°
x = `(140^circ)/2` = 70°
x = 70°
Interior opposite angle = 70°, 70°
Sum of the three angles of a triangle = 180°
70° + 70° + Third angle = 180°
140° + Third angle = 180°
Third angle = 180° – 140° = 40°
∴ Interior angle are 40°, 70°, 70°.
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