Question

if ( mangle msn = 106^{circ} ), then what is ( mangle lsp )?

Explanation:

Step1: Vertical angles

Vertical angles are equal. $\angle MSN$ and $\angle 5$ are vertical angles. So $m\angle5 = m\angle MSN=106^{\circ}$.

Step2: Linear - pair angles

$\angle5$ and $\angle LSP$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So $m\angle LSP=180^{\circ}-m\angle5$.
Substitute $m\angle5 = 106^{\circ}$ into the formula: $m\angle LSP=180^{\circ}- 106^{\circ}$.

Answer:

$74^{\circ}$