Parallel straight lines A B and CB intersect with the straight line EF at points M and N
Parallel straight lines A B and CB intersect with the straight line EF at points M and N, the angle АМN is 3 times less than the angle CNM Find all the formed non-developed corners.
Given: AB and SD are parallel straight lines;
the secant EF intersects these lines at points M and N, respectively;
angle CNM = 3 * angle AMN;
Find all formed corners?
1) Angles CNM and AMN are one-sided angles for parallel lines AB and SD and secant EF. The sum of their degree measures is 180 degrees:
angle CNM + angle AMN = 180;
3 * angle AMN + angle AMN = 180;
4 * angle AMN = 180;
angle AMN = 45 degrees. and angle CNM = 45 * 3 = 135 degrees.
2) angle АМN = angle МNД = 45 degrees and angle СNМ = angle ВМN = 135 degrees (as these angles are crosswise);
3) angle AME = angle EMB = 45 degrees; angle ВМN = angle ЕМА = 135 degrees and angle СNF = angle МNД = 45 degrees. and the angle СNМ = angle ДNF = 135 degrees (since these pairs of angles are vertical)