The interior opposite angles of a triangle are in the ratio 1: 3. Given that, anexterior angle of the triangle is 80°. Find the value of interior opposite angles.a) 40°, 120° b) 30°,60° c) 20°,60° d) 90°, 60°
Question
The interior opposite angles of a triangle are in the ratio 1: 3. Given that, anexterior angle of the triangle is 80°. Find the value of interior opposite angles.a) 40°, 120° b) 30°,60° c) 20°,60° d) 90°, 60°
Solution
The problem involves the concept of interior and exterior angles of a triangle.
Step 1: Understand that the sum of an interior angle and its adjacent exterior angle in a triangle is 180°.
Step 2: Given that an exterior angle of the triangle is 80°, its corresponding interior angle would be 180° - 80° = 100°.
Step 3: The problem states that the interior opposite angles of the triangle are in the ratio 1:3. This means that the two interior angles can be represented as x and 3x.
Step 4: In a triangle, the sum of all interior angles is 180°. So, x + 3x + 100° = 180°. Solving this equation gives x = 20°.
Step 5: Therefore, the two interior opposite angles are 20° and 60° (3x = 3*20° = 60°).
So, the correct answer is c) 20°,60°.
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