Question

(opt 1) day 8c: 1 - 7: lesson quiz (lms graded) sep 3 - 11:59 pm if two angles are supplementary to the same angle, then the two angles are congruent. the sum of the measures of a linear pair is 180°. angle addition postulate definition of perpendicular lines definition of linear pair transitive property of equality supplementary congruent angles are right angles. statement reason 1 ∠wzx ≅ ∠wzv given 2 ∠wzx and ∠wzv are a linear pair. 3 m∠wzx + m∠wzv = 180° 4 m∠wzx = m∠wzv = 90° 5 wy ⊥ vx

Explanation:

Step1: Identify linear - pair

By the definition of a linear pair, since $\angle WZX$ and $\angle WZV$ are adjacent and their non - common sides form a straight line, the reason for " $\angle WZX$ and $\angle WZV$ are a linear pair" is the Definition of Linear Pair.

Step2: Apply linear - pair property

The sum of the measures of a linear pair is $180^{\circ}$. So, for " $m\angle WZX + m\angle WZV=180^{\circ}$", the reason is The sum of the measures of a linear pair is $180^{\circ}$.

Step3: Use congruent and supplementary relationship

Given $\angle WZX\cong\angle WZV$ (i.e., $m\angle WZX = m\angle WZV$) and $m\angle WZX + m\angle WZV = 180^{\circ}$, substituting $m\angle WZV$ for $m\angle WZX$ gives $2m\angle WZX=180^{\circ}$, then $m\angle WZX = m\angle WZV = 90^{\circ}$. The reason is Supplementary congruent angles are right angles.

Step4: Define perpendicular lines

Since $m\angle WZX=m\angle WZV = 90^{\circ}$, by the definition of perpendicular lines (if the measure of the angle formed by two lines is $90^{\circ}$, the lines are perpendicular), the reason for $\overline{WY}\perp\overline{VX}$ is the Definition of Perpendicular Lines.

Answer:

Statement	Reason
2. $\angle WZX$ and $\angle WZV$ are a linear pair	Definition of Linear Pair
3. $m\angle WZX + m\angle WZV = 180^{\circ}$	The sum of the measures of a linear pair is $180^{\circ}$
4. $m\angle WZX=m\angle WZV = 90^{\circ}$	Supplementary congruent angles are right angles
5. $\overline{WY}\perp\overline{VX}$	Definition of Perpendicular Lines