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?*1 point80°,25°80°,75°25°,75°30°,70°
Question
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?*1 point80°,25°80°,75°25°,75°30°,70°
Solution
The sum of the measures of the interior opposite angles of a triangle is equal to the measure of the exterior angle. In this case, the exterior angle is 100°.
The problem states that the interior opposite angles are in the ratio 1:3. Let's denote the smaller angle as x and the larger angle as 3x.
So, we can set up the equation:
x + 3x = 100
Solving this equation gives:
4x = 100
x = 25
So, the smaller angle is 25° and the larger angle is 3 * 25 = 75°.
Therefore, the measures of the interior opposite angles are 25° and 75°.
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