Question

(b) problem 16: (first taught in lesson 30)
what is z in terms of x and y?
after you pick your answer press go.
a. z = 90 - x - y b. z = x + y - 180
c. z = 180 - x - y d. z = x + y - 90
e. z = x - y - 180

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is $180^{\circ}$. Let the third interior angle of the triangle be $a$. So, $a+(180 - x)+(180 - y)=180$.

Step2: Simplify the equation

First, expand the left - hand side: $a + 180 - x+180 - y=180$. Then, $a= x + y - 180$.

Step3: Use vertical angles property

Since $z$ and $a$ are vertical angles, and vertical angles are equal. So $z=a$. Thus, $z=x + y - 180$.

Answer:

C. $z = 180 - x - y$