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°.
