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Quadrilaterals are the polygons having four sides. Parallelogram, rectangle, square, rhombus, trapezium, and kite have some special properties. So, they are called special types of a quadrilateral. Some types of quadrilateral are as follows
Solution:
Let the angles of the quadrilateral be x°, 2x°, 3x° and 4x° respectively.
Here, x° + 2x° + 3x° + 4x° = 360°
or, 10x° = 360°
or, x° = \(\frac{360°}{10}\) = 36°
\(\therefore\) x° = 36°, 2 × 36° =72°, 3x° = 3 × 36° = 108° and 4x° = 4 × 36° = 144°.
Solution:
y° + 105° = 180° [Being the sum of a straight angle]
or, y° = 180° - 105° = 75°
Now, x° + (2x° + 10°) + 2x° + y° = 360° [The sum of the angles of a quadrilateral]
or, 5x° + 10° + 75° = 360°
or, 5x° = 360° - 85°
or x° = \(\frac{275°}{5}\) = 55°
\(\therefore\) x° = 55°, 2x° + 10° = 2×55° + 10° = 120°, 2x° = 2×55° = 110° and y° = 75°.
Solution:
Here, 2x° + 3x° + (2x+10)° + (x+30)° = 360° [Sum of the angles of quadrilateral]
or, (8x + 40)° = 360°
or, 8x° = 360° -40°
or, x = \(\frac{320°}{8}\) = 40°
\(\therefore\) 2x° = 2×40° = 80°, 3x° = 3×40° = 120°, (2x + 10)° = 2×40° + 10° = 90° and (x + 30)° = 40° + 30° = 70°
Solution:
Here,
w° = 25° [Being alternate angles]
x° = 20° [Being alternate angles]
Now, w° + 20° = 25° + 20° = 45°
x° + 25° = 20° + 25° = 45°
Again, y° + 45° = 180° [Being the sum of co-interior angles]
or, y° = 180° - 45°
or, y° = 135°
Also, z° = y° = 135° [Being the opposite angles of a parallelogram]
\(\therefore\) w° = 25°, x° = 20°, y° = z° = 135°.
The sides of the square are ______ .
In parallelogram the opposite sides are ______ .
Rhombus all sides are equal and opposite sides are ______ .
In the kite, opposite angles formed by each pair of unequal adjacent sides are _______ .
The diagonals of a rectangle are equal and they ______ each other.
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mid point theoram
finding value of x and y from figure
Jan 23, 2017
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