Question

example 5
parallelogram △hijk is shown.
the value of x is ________ because opposite angles in a parallelogram are congruent.
∠jih+∠ijk = ________ because they are supplementary angles.
125 + 22 + y=
which means the value of y is ________.
example 6
a parallelogram wxyz is

1. draw and label w
2. what is the an
3. what is the a

Explanation:

Step1: Use property of opposite angles

In parallelogram \(HIJK\), \(\angle I\) and \(\angle K\) are opposite angles. Since opposite - angles in a parallelogram are congruent, and \(\angle I = 125^{\circ}\), then \(x = 125\).

Step2: Use property of supplementary angles

Adjacent angles in a parallelogram are supplementary. \(\angle H\) and \(\angle I\) are adjacent angles, so \(\angle H+\angle I=180^{\circ}\).

Step3: Use angle - sum property of a triangle

In \(\triangle HJK\), the sum of the interior angles of a triangle is \(180^{\circ}\). We know one angle is \(22^{\circ}\) and \(\angle K = 125^{\circ}\). Let's find \(y\).
We have the equation \(22 + 125+y=180\).
\[y=180-(22 + 125)=180 - 147=33\]

Answer:

The value of \(x\) is \(125\) because opposite angles in a parallelogram are congruent. \(\angle H+\angle I = 180^{\circ}\) because they are supplementary angles. \(22 + 125+y=180\), which means the value of \(y\) is \(33\).