Question

lines ac and bd intersect at point o.
if ( mangle aod = (5x - 4)^circ ) and ( mangle boc = (4x + 5)^circ ), what is ( mangle boc )?
( 9^circ )
( 10^circ )
( 41^circ )
( 82^circ )

Explanation:

Step1: Set angles equal (vertical angles)

$5x - 4 = 4x + 5$

Step2: Solve for $x$

$5x - 4x = 5 + 4$
$x = 9$

Step3: Substitute $x$ into $\angle BOC$

$m\angle BOC = 4(9) + 5$

Answer:

41°