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°.
Answer:
breakdown the initial figure into 2 rectangle
and add their area
Answer:
C
Step-by-step explanation:
The slope is -1/3, so it will go down and to the right. Down 1, to the right 3 (rise over run!)
The y intercept is 2.
Answer:
25π - 24 cm²
Step-by-step explanation:
area of circle:
A = πr²
A = π(5²)
A = 25π
Area of triangle:
base = 6
height = 5 - 1 = 4
(1/2)(6 * 4) = 12
there are 2 triangles so unshaded area is 24 cm²
Area of shaded region = 25π - 24 cm²
Answer:
Hello
Step-by-step explanation:
The domain is limited with 2 lines parallel: -1 ≤ x ≤ 1
and the disk ? (inside of a circle) of center (0,0) and radius 2
