Find Angle α in Triangle ABC: Given Angles 27.7° and 41°

Find the size of angle α \alpha .

27.727.727.7AAABBBCCC41

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:02 Let's find the value of A.
00:05 Remember, the sum of angles in a triangle is always one hundred eighty degrees.
00:10 Now, plug in the known values from the problem, and work towards solving for A.
00:15 Next, gather like terms together.
00:18 Then, make sure to isolate A on one side of the equation.
00:25 And there you have it! That's the solution.

Step-by-step written solution

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1

Understand the problem

Find the size of angle α \alpha .

27.727.727.7AAABBBCCC41

2

Step-by-step solution

Note that the sum of the angles in a triangle is equal to 180 degrees.

Therefore, we can use the formula:

A+B+C=180 A+B+C=180

Then we will substitute in the known data:

α+27.7+41=180 \alpha+27.7+41=180

α+68.7=180 \alpha+68.7=180

Finally, we will move the variable to the other side while maintaining the appropriate sign:

α=180−68.7 \alpha=180-68.7

α=111.3 \alpha=111.3

3

Final Answer

111.3

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