Question

Find the value of X in the figure below:

• A. 80${}^{\circ }$
• B. 60${}^{\circ }$
• C. 70${}^{\circ }$
• D. 100${}^{\circ }$

Answer 1

The correct option is A 80${}^{\circ }$

We know that,

$\angle$ABC + $\angle$CAB + $\angle$ACB = 180${}^{\circ }$ (angle sum property)

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

⇒ $\angle$ACB = 40${}^{\circ }$

⇒ $\angle$KCL = $\angle$ACB = 40${}^{\circ }$ (vertically opposite angles)

⇒ $\angle$KCL + $\angle$CLK + $\angle$X = 180${}^{\circ }$

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

⇒ $\angle$X = 80${}^{\circ }$