Question

the fence uses vertical posts ( l ), ( m ), and ( o ) to hold parallel rails ( n ) and ( p ) together. if ( mangle1 = 94^{circ} ), what is ( mangle16 )?
a. ( 76^{circ} )
b. ( 86^{circ} )
c. ( 90^{circ} )
d. ( 94^{circ} )

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. \(86^{\circ}\)