Question

consider the diagram shown. find m∠amb

Explanation:

Step1: Identify vertical - angle relationship

$\angle JLC$ and $\angle KLD$ are vertical angles. Since $\angle JLC = 70^{\circ}$, then $\angle KLD=70^{\circ}$.

Step2: Use linear - pair property

$\angle KLD$ and $\angle KLE$ form a linear - pair. So $\angle KLE = 180^{\circ}-\angle KLD=180 - 70=110^{\circ}$.

Step3: Identify vertical - angle relationship for the final answer

$\angle AMB$ and $\angle KLE$ are vertical angles. So $m\angle AMB=\angle KLE$.

Answer:

$110^{\circ}$