Question

WXYZ is a parallelogram. Find the measure of angle Z

Answer 1

Given:

The figure of a parallelogram.

To find:

The measure of angle Z.

Solution:

We know that, the consecutive interior angles of a parallelogram are supplementary angles, it means there sum is 180 degrees.

In the given figure angle W and angle Z are supplementary angle. So,

$m\angle W+m\angle Z=180^\circ$

$(18b-11)^\circ+(9b+2)^\circ=180^\circ$

$(27b-9)^\circ=180^\circ$

$(27b-9)=180$

Adding 9 on both sides, we get

$27b=180+9$

$27b=189$

$b=\dfrac{189}{27}$

$b=7$

Now,

$m\angle Z=(9b+2)^\circ$

$m\angle Z=(9(7)+2)^\circ$

$m\angle Z=(63+2)^\circ$

$m\angle Z=65^\circ$

Therefore, the correct option is C.