the fence uses vertical posts ( l ), ( m ), and ( o ) to hold parallel rails ( n ) and ( p ) together. if (…

the fence uses vertical posts ( l ), ( m ), and ( o ) to hold parallel rails ( n ) and ( p ) together. if ( mangle1 = 94^{circ} ), what is ( mangle16 )?\na. ( 76^{circ} )\nb. ( 86^{circ} )\nc. ( 90^{circ} )\nd. ( 94^{circ} )

the fence uses vertical posts ( l ), ( m ), and ( o ) to hold parallel rails ( n ) and ( p ) together. if ( mangle1 = 94^{circ} ), what is ( mangle16 )?\na. ( 76^{circ} )\nb. ( 86^{circ} )\nc. ( 90^{circ} )\nd. ( 94^{circ} )

Answer

Explanation:

Step1: Find the measure of ∠2

∠1 and ∠2 are supplementary angles (they form a linear pair). So, (m\angle2 = 180^{\circ}-m\angle1) Substitute (m\angle1 = 94^{\circ}) (m\angle2=180 - 94=86^{\circ})

Step2: Use the property of parallel lines

Since rails (n) and (p) are parallel and posts (l,m,o) are transversals. ∠2 and ∠16 are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are equal. So, (m\angle16=m\angle2)

Answer:

B. (86^{\circ})