Question

Complete the table below. If it is possible to work out the measure of the angle, write it down and show your method. If it is not possible, explain how you know.
Angle: W X Y Z

Is it possible to find the measure of the angle? If so, what is it?

Explain carefully how you decided.

Answer 1

Answer:

∠W = 70°

∠X = 70°

∠Y = 40°

∠Z = 40°

Step-by-step explanation:

∠W = 70°      because they are alternate interior angles

∠Y = 180° - 70° + 70° = 40°       because all the interior angles of a triangle add up to 180°

∠X = 180° - 70° - ∠Y = 70°

∠Z = ∠Y + ∠70° - ∠W = 40°

Answer 2

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°.