如图，在$\triangle ABC$中，$∠A=20^{\circ}$，$∠ABC$与$∠ACB$的角平分线交于$D_{1}$， $∠ABD_{1}$与$∠ACD_{1}$的角平分线交于点$D_{2}$，依此类推，$∠ABD_{4}$与$∠ACD_{4}$的角平分线交于点$D_{5}$，则$∠BD_{5}C$的度数是$($　　$)$