Question

ABCD is a parallelogram. Find the measure of x, y & z.​

Answer 1

Answer:

x =100°, y = 35° and z = 45°

Step-by-step explanation:

First, We all know that the line-in-between is an Angle-Bisector. An Angle-Bisector divides an angle in half,so as The Angle opposite z is 45°,so angle z will be equal to 45°. We should also notice that the angle bisector divides the Parallelogram in 2 triangles.Now, the angle given outside is the Exterior Angle.An Exterior angle is always equal to the sum of Opposite interior angles of a triangle( In this case,I am talking about triangle CAB ).As we know the value of the Exterior angle as well as an Interior angle,we can subtract them both to get the value of the angle y. Explanation-

Exterior angle = Opposite Interior angle+ Another Opposite interior angle.

Shift any opposite interior angle to the left,and as the this angle's value is positive,it will turn negative.So,

Exterior Angle - Opposite Interior angle =

Opposite Interior angle.

So, 80° - 45° = 35° = Angle Y.

Now,the sum of angles of a triangle is 180°.So,

Explanation-

180° = angle opposite z + angle opposite y( Which will be equal to y,because of the Angle-Bisector and it's the same case for angle opposite z. )

So,Angle x will be equal to the number obtained by subtracting the sum of the values of other angles of triangle DAC from 180° .So,

45° + 35° = 80°.

Then, 180° - 80° = 100° = Angle x.

Hope You liked My Answer. Please mark my answer as the Brainliest Answer.BTW,I wrote this all myself,not from some book. I hope you now know how to solve this very easy question.Ta-Ta!