The angle N of the triangle MNK is 3 times the angle M, and the angle K is 55 degrees larger
| July 14, 2021 | education
The angle N of the triangle MNK is 3 times the angle M, and the angle K is 55 degrees larger than the angle M. Find the angles of the triangle.
Given: ∠N = 3 * ∠M, ∠K = ∠M + 55 °. We have: 3 * ∠M + ∠M + 55 ° + ∠M = 180 ° or 5 * ∠ M = 125 °, whence ∠M = 125 ° / 5 = 25 °, ∠K = ∠M + 55 ° = 25 ° + 55 ° = 80 °, ∠N = 3 * ∠M = 3 * 25 ° = 75 °.
Answer: ∠M = 25 °, ∠K = 80 °, ∠N = 75 °.
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