Find adjacent angles if one-third of one is equal to one-ninth of the other.

| August 5, 2021 | education

Let’s denote one adjacent angle by x, and the other by y. Adjacent angles have a common vertex and a common side, together they make up an unfolded angle, so their sum is 180 degrees: x + y = 180. By condition it is given that: (1/3) * x = (1/9) * y. We get a system of linear equations: x + y = 180; (1/3) * x = y / 9. In the first equation, we express x through y: x = 180 – y. Substitute the obtained value of x into the second equation: (1/3) * (180 – y) = y / 9. Solve the resulting equation: (180 – y) / 3 = y / 9; 3y = 9 * (180 – y) (the main property of the “cross to cross” proportion); 3y = 1620 – 9y; 12y = 1620; y = 1620/12; y = 135 degrees. Substitute the resulting y value into the first equation: x + y = 180; x + 135 = 180; x = 180 – 135; x = 45 degrees.
Answer: x = 45 degrees, y = 135 degrees.



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