One of the angles formed at the intersection of two straight lines is 2 times the sum of the adjacent angles Find these angles.
To solve this problem, we introduce two conditional variables “X” and “Y”, through which we denote the values of the larger and smaller adjacent angles, respectively.
Consider the fact that the sum of adjacent angles is 180 degrees.
Then, based on the data of the problem, we compose the following equations:
1) X + Y = 180;
2) X / (Y + Y) = 2.
Solving this equation, we get X = 180 – Y.
Substituting X into the second equation, we get 180 – Y = 4Y or 5Y = 180 or Y = 36 degrees.
Therefore, X will be equal to 36 x 4 = 144 degrees.
Answer: Adjacent angles are 144 degrees and 36 degrees.
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