Answer:
x=38 degrees, y=41 degrees, z=97 degrees
Explanation:
The Triangle Angle-Sum Theorem states that all interior angles of a triangle will add up to 180 degrees.
Look at the triangle to the right. The missing value of x will complete the theorem, therefore the equation 59+83+x=180 will find x. x=38 when we solve the equation.
The triangle on the left has two missing variables, but since angles z and 83 degrees are supplementary to each other, we can make another equation z+83=180 since supplementary angles add up to 180 degrees. z=97 when we solve the equation.
Since we have z, we can now find the value of y given the Triangle Angle-Sum Theorem. The equation would be 42+97+y=180 so we can solve for y. y=41 when we solve the equation.