Question

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

Explanation:

Step1: Vertical angles property

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

Step2: Linear - pair (supplementary angles)

$\angle5$ and $\angle LSP$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. Let $x = m\angle LSP$. Then $x + 106^{\circ}=180^{\circ}$.

Step3: Solve for $x$

Subtract $106^{\circ}$ from both sides of the equation $x+106^{\circ}=180^{\circ}$. So, $x=180^{\circ}- 106^{\circ}$.

Answer:

$74^{\circ}$