Question

One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the

third angle is 50 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.
Answer: The LARGEST angle has a measure of
degrees.
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Answer 1

The smallest angle in the triangle is 26 degrees. The largest angle is 76 degrees.

Step-by-step explanation:

Let's denote the smallest angle as x degrees.

According to the given information, one angle in the triangle is three times as large as the smallest angle, so it can be expressed as 3x.

The measure of the third angle is 50 degrees more than the smallest angle, so it can be expressed as x + 50.

Since the sum of the angles in a triangle is always 180 degrees, we can set up the following equation:

x + 3x + (x + 50) = 180

Simplifying the equation gives us:

5x + 50 = 180

Subtracting 50 from both sides:

5x = 130

Dividing both sides by 5:

x = 26

Therefore, the smallest angle is 26 degrees. Now we can find the largest angle by substituting x into the equation for the third angle:

Largest angle = x + 50 = 26 + 50 = 76 degrees.

Learn more about Triangle angles