Question

Find the value of $x$.

• A. ${20}^{\circ }$
• B. ${80}^{\circ }$
• C. ${60}^{\circ }$

Answer 1

$\angle$EBC = $\angle$BAC + X (external angle property)
120${}^{\circ }$ = 100${}^{\circ }$ + X
So, X = 20${}^{\circ }$

$\angle$ABO + $\angle$BAO + $\angle$AOB = 180${}^{\circ }$ (angle sum property)

⇒ 90${}^{\circ }$ + 50${}^{\circ }$ + $\angle$AOB = 180${}^{\circ }$

⇒ $\angle$AOB = 40${}^{\circ }$

⇒ $\angle$KOL = $\angle$AOB = 40${}^{\circ }$ (vertically opposite angles)

⇒ $\angle$KOL + $\angle$OLK + $\angle$X = 180${}^{\circ }$

⇒ 40${}^{\circ }$ + 60${}^{\circ }$ + $\angle$X = 180${}^{\circ }$

⇒ $\angle$X = 80${}^{\circ }$

As $\angle$AOB = $\angle$DOE (vertically opposite angles)
So, $\angle$X = 60${}^{\circ }$