Question

in figure ABCD is a isosceles trpezium, find x, y and z

Answer 1

Answer:

x = 110°

y = 110°

z = 70°

Step-by-step explanation:

We know that the sum of the angles of any quadrilateral figure is 360°. (a)

Now, in an insosceles trapezium, the non paired angles (in this case angle A and C, and angle B and D) are always supplementary (that is, their sum is equal to 180°) (b)

So, since angle A is 70° (given),

angle C has to be (180-70)° = 110°.

We also know that the base angles (in this case angle A and B) of an insosceles trapezium are always equal. (c)

So, since angle A is 70°, angle B is also 70°.

Now, we have have measure of angle B. So, we can easily find out the measure of angle D considering the (b)

Angle B is 70°, so angle D is (180-70)° = 110°

Therefore,

x = 110° (measure of angle D)

y = 110° (measure of angle C)

z = 70° (measure of angle B)

Hope it is clear :)