Question

Find the values of x, y, and z. The diagram is not to scale. · 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

Answer 1

The values of x, y, and z are x = 86 degrees, y = 94 degrees, and z = 75 degrees.

Step-by-step explanation:

To find the values of x, y, and z, we can apply the properties of triangles and angle sums. In the left triangle, the sum of angles is 35 degrees + x degrees + 59 degrees = 180 degrees.

Simplifying, we get x = 86 degrees. Similarly, in the right triangle, the sum of angles is 11 degrees + y degrees + z degrees = 180 degrees. Simplifying, we get y + z = 169 degrees.

Since we know y + z = 169 degrees and y = 94 degrees, we can substitute the value of y into the equation and solve for z. z + 94 = 169, so z = 169 - 94 = 75 degrees.

Therefore, the values of x, y, and z are x = 86 degrees, y = 94 degrees, and z = 75 degrees.