In the NPT triangle, the angle P is 88 degrees, and the angle N is 5 times less

In the NPT triangle, the angle P is 88 degrees, and the angle N is 5 times less than the external angle at the vertex T. Find all unknowns corners.

Triangle NPT: <P = 88 °; A) <(180 ° – <T) = 5 * (<N); P + <N + <T = 180 °; We apply all these equalities:

<N + <T = 180 ° – 88 ° = 92 °; B) 92 ° – <T = <N; compare A) and B), we get: 180 ° + <N – 92 ° = 5 * <N; 4 * <N = 88 °; <N = 22 °; <P = 180 ° – 88 ° – 22 ° = 70 °.

Answer: <N = 88 °; <P = 70 °.