Question

Find the values of x, y and z from the given parallelograms.please help please it's a request ​

Answer 1

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°