Question

lines ( ell ) and ( m ) are intersected by transversal ( t ) and ( ell parallel m ).
select all the angles that are supplementary to ( angle 7 ).

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Identify adjacent angles

\(\angle5\) and \(\angle7\) are adjacent angles forming a linear pair. So, \(\angle5+\angle7 = 180^{\circ}\).

Step3: Use the properties of parallel lines and transversals

Since \(\ell\parallel m\), \(\angle4\) and \(\angle5\) are congruent (alternate interior angles). Also, \(\angle6\) and \(\angle4\) are vertical angles (so \(\angle6=\angle4\)).
\(\angle3\) and \(\angle4\) form a linear pair (\(\angle3+\angle4 = 180^{\circ}\)), and because \(\angle4=\angle5\), we can substitute. Also, \(\angle6\) and \(\angle7\) form a linear pair (\(\angle6+\angle7=180^{\circ}\))

Answer:

\(\angle5\), \(\angle6\), \(\angle3\), \(\angle4\)