Answer:
(ii) (x, y, z) = (110°, 30°, 30°)
(iii) (x, y, z) = (110°, 70°, 70°)
Step-by-step explanation:
The things you need to know and use are ...
Opposite angles of a parallelogram are congruent.
Adjacent angles of a parallelogram are supplementary.
Alternate interior angles between a transversal and parallel lines are congruent.
Corresponding angles where a transversal crosses parallel lines are congruent.
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(ii) Angles B and D are opposite, so congruent:
x = 110°
Angle DAB is supplementary to angle B, so is 70°. That means z is ...
z = 70° -40° = 30°
Angle y is "alternate interior" relative to z, so is congruent to z:
y = 30°
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(iii) Angle x is adjacent to angle N, so is supplementary to 70°.
x = 180° -70° = 110°
Angle y is opposite angle N, so is congruent.
y = 70°
Angle z is corresponding to angle N, so is congruent. (It is also "alternate interior" with respect to angle y, so is congruent to y.)
z = 70°
