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 = 94, z = 75
x = 86, y = 75, z = 94
x = 86, y = 75, z = 94
x = 75, y = 94, z = 86
x = 75, y = 94, z = 86
x = 75, y = 86, z = 94
None of the given options is correct. The values of x, y, and z cannot be determined from the information given.
To find the values of x, y, and z, we can use the fact that the angles in any triangle add up to 180 degrees.
In the left triangle, we have angles of 35 degrees, x degrees, and 59 degrees. Since the angles in a triangle add up to 180 degrees, we can write the equation:
35 + x + 59 = 180
Simplifying the equation, we get:
x + 94 = 180
x = 180 - 94
x = 86
So, the value of x is 86 degrees.
In the right triangle, we have angles of 11 degrees, y degrees, and z degrees. Using the same reasoning, we can write the equation:
11 + y + z = 180
There is no further information given, so we cannot solve for y and z. Therefore, we cannot determine the exact values of y and z.