Answer:
- w = 70° . . . . alternate interior angles
- x = 70° . . . . alternate interior angles
- y = 40° . . . . angle sum in a triangle
- z = ?? . . . . not enough information
Explanation:
The alternate interior angles theorem, and the angle sum theorem can be used here.
Alternate interior angles
Alternate interior angles are found on either side of a transversal where it crosses a pair of parallel lines. They are between the parallel lines. Their vertices are at the junction of the transversal and the parallel lines. Alternate interior angles are congruent.
In this diagram, there are two pairs of alternate interior angles where the two transversals AD and BD cross parallel lines AB and CD.
At points A and D, the alternate interior angles are 70° and x, respectively. This tells you ...
x = 70° . . . . alternate interior angles theorem
At points B and D, the alternate interior angles are w and 70°, respectively. This tells you ...
w = 70° . . . . alternate interior angles theorem
Angle sum
The angle sum theorem tells you the sum of angles in a triangle is 180°. This fact can be used to find the measure of angle y.
70° +w +y = 180°
y = 180° -70° -w = 110° -70°
y = 40° . . . . angle sum theorem
There is not enough information to determine the measure of angle z.
z = indeterminate