Question

In the diagram A, B, C and D are points on the circumference of a circle. $\angle ABD={40}^o$ and angle $\angle AXB={105}^o$. The magnitude of $\angle XDC$ is

• A. ${35}^o$
• B. ${40}^o$
• C. ${45}^o$
• D. ${50}^o$
• E. ${55}^o$

Answer 1

Answer: (A)

${35}^o$

$\angle ABD=\angle ACD$ because they are angles made by the same arc AD

$⟹\angle ACD=40$

$\angle BXA=\angle CXD=105$

In $△XCD$

$\angle XCD+\angle CDX+\angle DXC=180$

$\angle XDC=180–105–40=35$