Question

in the figure, lines m and n are parallel. if ( mangle6 = 97^{circ} ), what is ( mangle5 )? ( 83^{circ} ) ( 90^{circ} ) ( 97^{circ} ) ( 180^{circ} )

Explanation:

Step1: Use the linear - pair relationship

Angles that form a linear pair are supplementary. That is, if two angles form a linear pair, then \(m\angle x + m\angle y=180^{\circ}\).
Here, \(\angle5\) and \(\angle6\) form a linear pair. So, \(m\angle5 + m\angle6=180^{\circ}\).

Step2: Substitute the value of \(m\angle6\)

Given \(m\angle6 = 97^{\circ}\). Substitute into the equation \(m\angle5+97^{\circ}=180^{\circ}\).
Then, solve for \(m\angle5\): \(m\angle5=180^{\circ}-97^{\circ}\).

$$m\angle5 = 83^{\circ}$$

Answer:

\(83^{\circ}\)