Find the values of x, y, and z. The diagram is not to scale.
The image of a larger triangle divided into two smaller triangles is shown.· A larger triangle is shown with a segment drawn from its top vertex to its opposite side forming two smaller triangles.
· The triangle formed on the left has labeled angles of 35 degree sign, x degree sign, and 59 degree sign in a clockwise order with the 35 degree sign angle at the top.
· The triangle formed on the right has labeled angles of 11 degree sign, y degree sign, and z degree sign in a clockwise order with the 11 degree sign angle at the top.
(1 point)
Responses
x = 86, y = 94, z = 75
x = 86, y = 75, z = 94
x = 75, y = 94, z = 86
x = 75, y = 86, z = 94
The correct answer is:
x = 75, y = 94, z = 86
To find the values of x, y, and z, we can use the fact that the angles of a triangle add up to 180 degrees.
In the triangle on the left, we have an angle of 35 degrees and an angle of 59 degrees. Adding these two angles together gives us:
35 + 59 = 94 degrees.
So, x = 94 degrees.
In the triangle on the right, we have an angle of 11 degrees. To find the sum of the remaining two angles, we subtract 11 from 180:
180 - 11 = 169 degrees.
The sum of the remaining two angles is 169 degrees. We know that y is one of these angles, so y = 169 degrees.
We also know that the sum of the angles in a triangle is 180 degrees, so we can find z by subtracting the sum of the other two angles from 180:
180 - (11 + 169) = 180 - 180 = 0 degrees.
Therefore, z = 0 degrees.
So, the values of x, y, and z are:
x = 94 degrees
y = 169 degrees
z = 0 degrees.
Therefore, the correct answer is:
x = 94, y = 169, z = 0.