Answer:
w = 70°
x = 70°
y = 40°
z = 40°
Step-by-step explanation:
Notice that two sides of the figure are parallel to each other according to the arrow marking on both sides. This means that by definition this figure must be a parallelogram. This also means that the two other sides must be parallel as well so that there are also two sets of parallel sides.
There is also a transversal (line that cuts across two lines) of which are parallel, this forms different angles which are corresponding, alternate interior, alternate exterior, and supplementary.
70° at <BDC and w are alternate interior which means that they must be the same measure.
Therefore
w = 70°.
Since a parallelogram consists of 2 equal triangles, and we know that two angles are both 70° given that w is 70°, all interior angles must add up to 180° according to the triangle angle sum theorem. So 70° + 70° + y° = 180°.
140° + y° = 180°
–140° –140
Therefore
y = 40°.
Since angle x is exterior and adjacent of (next to) the two interior angles (70° and y), they are supplementary pairs which means that they add up to 180°, because they form a straight line.
Knowing that y is 40°,
x° + 40° + 70° = 180°.
x° + 110° = 180°
–110 –110
Therefore
x = 70°.
Now since angle z is alternate interior of angle y, alternate interior angles have the same measure by definition.
Given that we already know the measure of y = 40°. z must also be 40°
Therefore
z = 40°.
The picture in the attached figure
let
AB=x
we know that
perimeter of the figure=10*x
perimeter=42.5 cm
so
42.5=10*x
x=42.5/10
x=4.25 cm
area of the figure=area of rectangle +area of square
area of rectangle=4.25*(4.25*3)----> 54.1875 cm²
area of square=4.25²----> 18.0625 cm²
area of the figure=54.1875+18.0625-----> 72.25 cm²
the answer is72.25 cm²
12/35 cannot be simplified further. To check, divide each of them by the same number. If u cannot get a whole number for both, this means that your fraction cannot be simplified.
Thx!
