Question

select all the true statements. a. x = y b. x + y = 180 c. y = z d. x + z = 180 e. y + z = 180

Explanation:

Step1: Find the value of $x$

Use the exterior - angle property of a triangle. The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So $x=82 + 54=136$.

Step2: Analyze angle relationships

Since $y$ and $x$ are vertical angles, $y = x$ (vertical angles are equal). So $y = 136$. Also, $x$ and $z$ are a linear pair (they form a straight line), so $x+z = 180$ (linear - pair angles are supplementary).

Answer:

A. $x = y$ (True, because vertical angles are equal)
D. $x + z = 180$ (True, because they are a linear pair)