Question

consider the diagram shown. find m∠amb.

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. Angle $\angle JLC$ and the angle adjacent to $\angle AMB$ (let's call it $\angle KME$) are vertical - angles. Since $\angle JLC = 70^{\circ}$, then $\angle KME=70^{\circ}$.

Step2: Use linear - pair property

$\angle KME$ and $\angle AMB$ form a linear pair. A linear pair of angles is supplementary, meaning the sum of the two angles is $180^{\circ}$. Let $m\angle AMB = x$. Then $x + 70^{\circ}=180^{\circ}$.

Step3: Solve for $\angle AMB$

Subtract $70^{\circ}$ from both sides of the equation $x + 70^{\circ}=180^{\circ}$. We get $x=180^{\circ}-70^{\circ}=110^{\circ}$.

Answer:

$110^{\circ}$