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A triangle has one angle of 120 degrees and two equal angles. What is the measure of each of the equal angles?30 degrees90 degrees45 degrees60 degrees

Question

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Solution

1. ### Break Down the Problem

We have a triangle with one angle measuring 120120^\circ and two equal angles. We need to find the measure of each of the equal angles.

2. ### Relevant Concepts

The sum of all angles in a triangle is 180180^\circ. If one angle is 120120^\circ, we can denote the two equal angles as xx. The equation can be set up as:

120+x+x=180 120^\circ + x + x = 180^\circ

This simplifies to:

120+2x=180 120^\circ + 2x = 180^\circ

3. ### Analysis and Detail

  1. Start by isolating 2x2x:

2x=180120 2x = 180^\circ - 120^\circ 2x=60 2x = 60^\circ

  1. Now, solve for xx:

x=602 x = \frac{60^\circ}{2} x=30 x = 30^\circ

4. ### Verify and Summarize

Let's verify it by checking the sum of all angles:

120+30+30=180 120^\circ + 30^\circ + 30^\circ = 180^\circ

Thus, the calculations are correct, and each of the equal angles measures 3030^\circ.

Final Answer

Each of the equal angles measures 3030^\circ.

This problem has been solved

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