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If the measure of the angles in a triangle are in the ratio 3:4:5, the measure of an exterior angle of the triangle can not be

User Dontexist
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2 Answers

3 votes

Final answer:

The interior angles of a triangle with a 3:4:5 ratio are 45, 60, and 75 degrees. The corresponding exterior angles are 135, 120, and 105 degrees. Therefore, an exterior angle cannot be less than 105 degrees or more than 135 degrees.

Step-by-step explanation:

When considering a triangle, we know by definition that it is a three-sided figure lying on a plane with the sum of its interior angles totaling 180 degrees. Given the ratio of the interior angles as 3:4:5, we can find their actual measures by setting up an equation: 3x + 4x + 5x = 180 degrees, where x is a common multiplier for each ratio. Solving for x, we get x = 180 / (3+4+5) = 180 / 12 = 15 degrees. Therefore, the actual angle measures of the triangle are 45 degrees (3x), 60 degrees (4x), and 75 degrees (5x).

An exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Therefore, there are three possible exterior angles for this triangle: 135 degrees (180-45), 120 degrees (180-60), and 105 degrees (180-75). Any exterior angle of this triangle cannot be less than 105 degrees or more than 135 degrees based on these calculations.

User Noa Gani
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2 votes

Answer:

I would use photomath if you cant find your answer.

Step-by-step explanation:

User Min Soe
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