Question

consider the diagram shown. find m∠amb.

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. $\angle BJC$ and $\angle KLD$ are vertical - angles. $\angle BJC = 70^{\circ}$, so $\angle KLD=70^{\circ}$. Also, $\angle JLD = 110^{\circ}$ as it is a linear - pair with $\angle BJC$ ($70^{\circ}+110^{\circ}=180^{\circ}$).

Step2: Use the property of vertical - angles for $\angle AMB$

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

Answer:

$70^{\circ}$