Let's break down and solve questions (g) and (h) from the image:

(g) ABCD is a parallelogram.

• Angle $\angle A = 54^\circ$
• We need to find angles $x$ and $y$.

Parallelogram properties:

• Opposite angles are equal.
• Adjacent angles are supplementary (i.e., they add up to $180^\circ$).

Solution:

• Since $\angle A = 54^\circ$, its opposite angle is also $54^\circ$ (because opposite angles in a parallelogram are equal). $\angle C = 54^\circ$
• Now, the adjacent angle $\angle B$ is supplementary to $\angle A$. So: $\angle B + \angle A = 180^\circ$ $x + 54^\circ = 180^\circ$ $x = 180^\circ - 54^\circ = 126^\circ$
• The angle $y$ is opposite $\angle B$, so $y = x = 126^\circ$.

Thus:

• $x = 126^\circ$
• $y = 126^\circ$

(h) ABCD is a rectangle.

• Given: one angle is divided by diagonals, and we need to find the value of $x$.

Rectangle properties:

• All angles in a rectangle are $90^\circ$.
• Diagonals of a rectangle are equal and bisect each other.

Solution:

• The angle $\angle DAB$ is $90^\circ$ because it's a rectangle. Since the diagonals bisect the angle, both of the smaller angles formed at $A$ will be equal. $2x = 90^\circ$ $x = \frac{90^\circ}{2} = 45^\circ$

Thus:

• $x = 45^\circ$

Do you want more detailed steps for any of these solutions, or do you have any further questions?

Related Questions:

1. What are the properties of a rhombus, and how can they help solve angle problems?
2. How can the diagonals of a parallelogram help in determining unknown angles?
3. What role do the symmetry and equal diagonals of rectangles play in angle calculations?
4. How do you calculate the supplementary angle for various types of quadrilaterals?
5. What are the key properties of a kite, and how can they help solve geometry problems?

Tip: Always recall that in any parallelogram, adjacent angles add up to 180°. This property can quickly help you solve unknown angles!