Question

Find the values of the variables in the parallelogram. The diagram is not to scale.
A. x = 49, y = 29, z = 102
B. x = 29, y = 49, z = 131
C. x = 49, y = 49, z = 131
D. x = 29, y = 49, z = 102

Answer 1

D:
x is 29° because of the "opposite inside rule"

y is 49° because the parallelogram is broke up into 2 triangles meaning that each need to equal 180.° 29+49+102=180

z is congruent to the angle that's 102°

Answer 2

Answer:  The correct option is

(D) x = 29, y = 49, z = 102.

Step-by-step explanation:  We are given to find the values of the variables x, y and z in the parallelogram shown.

Let us label the given parallelogram as ABCD, shown in the attached figure.

Here,

m∠CAB = 29°,  m∠ABC = 102°.

Now, since AB is parallel to CD and AC is a transversal. So,

$m\angle CAB = m\angle ACD\\\\\Rightarrow m\angle ACD = 29^\circ\\\\\Rightarrow x=29.$

Now, in triangle ABC, we have

$m\angle ABC+m\angle ACB+m\angle BAC=180^\circ~~~~~~~~\textup{[angle sum property of a triangle]}\\\\\Rightarrow 102^\circ+y^\circ+29^\circ=180^\circ\\\\\Rightarrow y^\circ+131^\circ=180^\circ\\\\\Rightarrow y^\circ=180^\circ-131^\circ\\\\\Rightarrow y^\circ=49^\circ\\\\\Rightarrow y=49.$

Again, we know that the measures of the opposite angles of a parallelogram are equal.

So,

$m\angle ADC=m\angle ABC\\\\\Rightarrow z^\circ=102^\circ\\\\\Rightarrow z=102.$

Thus, the required values are

x = 29, y = 49, z = 102.

Option (D) is CORRECT.