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The image contains a mathematical problem related to a parallelogram and the equation of a line. Here is the breakdown of the tasks given in the problem:

1. The first question mentions that "ABCD is a parallelogram." We are required to find the values of \( x \) and \( y \) based on the angles provided in the diagram.

2. The second question asks to "write the given equation in the form \( y = mx + c \)" and find the values of \( m \) and \( c \).

Let's first tackle the question related to the parallelogram.

### Parallelogram Properties:
- Opposite angles in a parallelogram are equal.
- Adjacent angles are supplementary (i.e., their sum is \( 180^\circ \)).

From the diagram, we can see that one angle is given as \( 90^\circ \), and two angles are marked as \( 2y + 5x \) and \( 100^\circ \).

### Step 1: Use the supplementary angle property.
Let's set up the equation for supplementary angles (as adjacent angles in a parallelogram sum to \( 180^\circ \)):
\[
(2y + 5x) + 100^\circ = 180^\circ
\]
This simplifies to:
\[
2y + 5x = 80^\circ
\]

### Step 2: Use the opposite angle property.
Since the opposite angles of a parallelogram are equal, the angle marked \( 90^\circ \) opposite another angle means the other angle is also \( 90^\circ \).

### Second Question: Equation of a Line
You are asked to express the equation in the form \( y = mx + c \), and find the values of \( m \) (the slope) and \( c \) (the intercept). The data related to this equation seems incomplete, so please provide any missing points or the equation to help clarify it.

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If you would like more details or explanations, feel free to ask!

### Further Questions:
1. How do we calculate the angles in any quadrilateral?
2. What are some properties of the slopes of parallel and perpendicular lines?
3. What are the supplementary and opposite angle properties of parallelograms?
4. How can we find the equation of a line using two points?
5. How do the values of \( m \) and \( c \) affect the graph of a line?

### Tip:
In parallelograms, always remember that opposite sides are equal and parallel, and opposite angles are also equal. This can help solve many problems related to angles.

If the given figure ABCD is a parallelogram, find the value of x and y. Also, write the given equation in y = mx + c form and find the values of m and c.

Learn how to solve for x and y in a parallelogram, using the properties of angles and supplementary relationships. Also, understand how to write equations in the form y = mx + c, and determine the values of m and c.

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