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12. In a triangle JKL, 3angleJ = 4angleK = 5angleL, find the measures of all the angles of the triangle.

User Deirdra
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Final answer:

In a triangle JKL, the measures of angles J, K, and L are 18 degrees, 72 degrees, and 90 degrees, respectively.


Step-by-step explanation:

In a triangle JKL, let's say that the measure of angle J is x degrees. According to the given information, we know that angle K is 4 times angle J, so angle K is 4x degrees. Similarly, angle L is 5 times angle J, so angle L is 5x degrees.

The sum of the measures of angles in a triangle is always 180 degrees. Using this information, we can write the equation: angle J + angle K + angle L = 180.

Substituting the values we found, we have: x + 4x + 5x = 180.

Combining like terms, we get: 10x = 180.

Dividing both sides by 10, we find that x = 18.

Therefore, angle J = 18 degrees, angle K = 72 degrees, and angle L = 90 degrees.


Learn more about Triangle angles

User Stephen Rodriguez
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