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Define quadrilateral, find parallelogram angles w, x, y given z=98°, and calculate trapezium area given dimensions.
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15. Define the term quadrilateral and state two examples.
A quadrilateral is a polygon with four straight sides and four vertices. Its interior angles sum to .
Examples: Square, Rectangle.
17. If find angles and .
Assuming the given quadrilateral is a parallelogram based on the diagram:
Step 1: In a parallelogram, opposite angles are equal.
Given . Angle is opposite to .
Step 2: In a parallelogram, consecutive angles are supplementary (add up to ).
Angle is consecutive to .
Step 3: Angle is opposite to .
18. Calculate the area of the following:
Part a· 2 steps
Trapezium
Identify the lengths of the parallel sides ( and ) and the height ().
Use the formula for the area of a trapezium.
Part b
Square
Identify the side length ().
Use the formula for the area of a square.
Part c
Parallelogram
Identify the base () and the given angle and side.
Calculate the height () using trigonometry.
Use the formula for the area of a parallelogram.
(Approximately )
19. A quadrilateral has angles . Find the value of .
The sum of the interior angles of a quadrilateral is .
Set up the equation with the given angles.
Combine like terms.
Solve for .
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