Question

In the diagram A, B, C and D are points on the circumference of a circle. $\angle ABC={115}^o,\angle BAD={70}^o$ and $AB=AD$. The magnitude of $\angle ACD$ is

• A. ${45}^o$
• B. ${55}^o$
• C. ${40}^o$
• D. ${70}^o$
• E. ${50}^o$

Answer 1

The correct option is B ${55}^o$

In $△ABD$

$AB=AD$ is given

$⟹\angle ABD=\angle ADB$

$\angle ABD+\angle ADB+\angle BAD=180$

$2\angle ABD=180–70$

$\angle ABD=55$

$\angle ABD$ and $\angle ACD$ are made by the same arc AD

$⟹\angle ABD=\angle ACD=55$