Question

select the correct answer form each drop - down menu.
given: ( mangle woz = 90^{circ} )
prove: ( mangle wox = 90^{circ} )
complete the proof.
suppose ( mangle wox
eq90^{circ} ). by the
( angle wox ) is supplementary to ( angle woz ). therefore,
( mangle wox + mangle woz = 180^{circ} ). by the assumption and the substitution property of equality, ( 90^{circ}+mangle woz
eq180^{circ} ). using the
subtraction property of equality, the measure of angle woz
90°, which contradicts the given. therefore, the assumption is
not true, and ( mangle wox = 90^{circ} ).

Explanation:

Step1: Use the definition of supplementary angles

Two angles are supplementary if the sum of their measures is \(180^{\circ}\). In the figure, \(\angle WOX\) and \(\angle WOZ\) form a linear - pair. By the linear - pair postulate (which states that if two angles form a linear pair, then they are supplementary), \(\angle WOX\) is supplementary to \(\angle WOZ\). So the first blank should be filled with "linear - pair postulate".

Step2: Analyze the equation \(90^{\circ}+m\angle WOZ

eq180^{\circ}\)
Starting from \(m\angle WOX + m\angle WOZ=180^{\circ}\), if \(m\angle WOX
eq90^{\circ}\), substituting \(m\angle WOX\) with a non - \(90^{\circ}\) value (say \(x
eq90^{\circ}\)) gives \(x + m\angle WOZ = 180^{\circ}\). If we assume \(x
eq90^{\circ}\), then from \(x + m\angle WOZ = 180^{\circ}\), we can rewrite it as \(m\angle WOZ=180^{\circ}-x\). Since \(x
eq90^{\circ}\), \(180 - x
eq90^{\circ}\). So, using the subtraction property of equality (\(a + b=c\Rightarrow b=c - a\)), from \(m\angle WOX+m\angle WOZ = 180^{\circ}\) (where \(m\angle WOX
eq90^{\circ}\)), we get \(m\angle WOZ=180^{\circ}-m\angle WOX
eq90^{\circ}\).

Answer:

First blank: linear - pair postulate; Second blank: does not equal.