Question

Choose the correct answer from the alternatives given :
In the figure given below what is the measure of $\angle BYX$?

• A. ${85}^{\circ }$
• B. ${50}^{\circ }$
• C. ${45}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

Answer: (A)

${85}^{\circ }$

We know that angles in the same segment of a circle are equal.
:. $\angle$XBY = $\angle$XAY = ${45}^{\circ }$
In $\Delta$BXY, $\angle$BXY + $\angle$XBY - $\angle$BYX = ${180}^{\circ }$
$\Rightarrow {50}^{\circ }+{45}^{\circ }+\angle BYX={180}^{\circ }$ (:. $\angle BXY={50}^{\circ }$)
$\Rightarrow \angle BYX={180}^{\circ }-{95}^{\circ }={85}^{\circ }$