Step-by-step explanation:
p)
in a very similar way, as the sum of all 4 angles in a triangle is always 180°, so is the sum of all angles in a quadrilateral (a polygon with 4 sides) 360°.
just look at rectangles at special representatives of such quadrilaterals.
now that we know this, we can simply say, the sum of all angles in our shape must be 360° :
(8x + 2) + (4x + 2) + (x - 2) + (5x -2) =
= 18x = 360
x = 20
A = 8×20 + 2 = 162°
B = 4×20 + 2 = 82°
C = 5×20 - 2 = 98°
D = 20 - 2 = 18°
a trapezium has the following properties (in the UK):
like other quadrilaterals, the sum of all the four angles of the trapezium is equal to 360°.
a trapezium has two parallel sides and two non-parallel sides.
the diagonals of a regular trapezium bisect each other.
in the USA for example the request for 2 parallel sides does not exist.
we have proven the point with the angle sum.
the other 2 are given by the diagram.
so, yes, it is a trapezium.
q)
the sum of all interior angles of a polygon is
(n - 2) × 180°
n being the number of d sides.
we have here a regular pentagon (5 equal sides).
the size of the angle at any vertex is then
(5 - 2) × 180 / 5 = 3 × 180 / 5 = 3×36 = 108°.
so, theta = 108°.
alpha + beta = 108°
ABE is an isoceles triangle.
so, beta = angle 1
beta + angle 1 + theta = 180
2×beta + 108 = 180
2×beta = 72
beta = 36°
therefore,
alpha = 108 - beta = 108 - 36 = 72°
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