Question

consider the diagram shown. find m∠amb.

Explanation:

Step1: Identify vertical - angles

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

Step2: Use linear - pair property

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

Step3: Identify vertical - angles again

$\angle GLK$ and $\angle AMB$ are vertical - angles. Since vertical - angles are congruent, $m\angle AMB=\angle GLK$.

Answer:

$110^{\circ}$