If an exterior angle of a triangle measure 100° and its interior opposite angles are in the ratio 1:3.What is the meaure of its interior opposite angles?
Question
If an exterior angle of a triangle measures 100° and its interior opposite angles are in the ratio 1:3, what is the measure of its interior opposite angles?
Solution
The sum of an exterior angle and its corresponding interior angle of a triangle is 180°.
Given that the exterior angle is 100°, the sum of the two interior opposite angles is 180° - 100° = 80°.
The problem states that the two interior opposite angles are in the ratio 1:3. Therefore, we can divide the total of 80° into 4 parts (1 part for the smaller angle and 3 parts for the larger angle).
Each part is therefore 80° / 4 = 20°.
So, the smaller interior angle is 20° and the larger interior angle is 20° * 3 = 60°.
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