Question

Two lines intersect and create four angles one angle is 70 degrees the angle x and y are both linear angle pairs with 70 degrees the angles x is a vertical angle to 70 degrees find the degrees of the angles x and y and z.

Answer 1

The angles x, y, and z are 70 degrees, 110 degrees, and 110 degrees, respectively.

Explanation:

If one angle is 70 degrees, then its corresponding angle will also be 70 degrees. Therefore, the two linear angle pairs with 70 degrees are:

70 degrees and its corresponding angle (also 70 degrees)

x degrees and y degrees, where x and y add up to 180 degrees (because they are linear angle pairs)

Since x is a vertical angle to 70 degrees, it is also equal to 70 degrees. Therefore:

x = 70 degrees

y = 180 - x = 180 - 70 = 110 degrees

To find the angle z, we can use the fact that the sum of the angles around a point is 360 degrees. Since the two lines intersect and create four angles, the angles around the point where they intersect must add up to 360 degrees. Therefore:

z + 70 + 70 + 110 = 360

z + 250 = 360

z = 110 degrees

Therefore, the angles x, y, and z are 70 degrees, 110 degrees, and 110 degrees, respectively.