Question

prove
\\( \angle z \\) is a right angle

what geometric reason justifies the transition from statement 2 and 3 to statement 4?
supplemental right angles theorem
substitution
congruent right angles theorem
vertical angles theorem

Explanation:

Step1: Analyze the relationship between angles

From statement 2, we know that $\angle X+\angle Y = 180^{\circ}$ (supplementary angles). From statement 3, $\angle X\cong\angle Y$, which means $\angle X=\angle Y$.

Step2: Substitute and solve

Substitute $\angle Y$ with $\angle X$ in the equation $\angle X+\angle Y = 180^{\circ}$. We get $\angle X+\angle X=180^{\circ}$, or $2\angle X = 180^{\circ}$. Solving for $\angle X$, we have $\angle X = 90^{\circ}$, so $\angle X$ is a right - angle. This process uses substitution.

Answer:

Substitution