Question

lines ac and bd intersect at point o.
if ( mangle aod=(10x - 7)^{circ} ) and ( mangle boc=(7x + 11)^{circ} ), what is ( mangle boc )?
( 6^{circ} )
( 53^{circ} )
( 89^{circ} )
( 106^{circ} )

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(m\angle AOD=m\angle BOC\).
\(10x - 7=7x + 11\)

Step2: Solve for \(x\)

Subtract \(7x\) from both sides: \(10x-7x - 7=7x-7x + 11\), which gives \(3x-7 = 11\).
Add \(7\) to both sides: \(3x-7 + 7=11 + 7\), so \(3x=18\).
Divide both sides by \(3\): \(x=\frac{18}{3}=6\).

Step3: Find \(m\angle BOC\)

Substitute \(x = 6\) into \(m\angle BOC=(7x + 11)^{\circ}\).
\(m\angle BOC=(7\times6 + 11)^{\circ}=(42+11)^{\circ}=53^{\circ}\)

Answer:

\(53^{\circ}\)