Question

In the following figure, O is the center of the circle and AB is a diameter. C and D are points on the circumference of the circle such that $\angle CAB={35}^0$ and $\angle ABD={55}^0$, then the measures of angles CAD and CBD are

• A. $\angle CAD={110}^0$ and $\angle CBD={70}^0$
• B. $\angle CAD={90}^0$ and $\angle CBD={90}^0$
• C. $\angle CAD={80}^0$ and $\angle CBD={100}^0$
• D. $\angle CAD={70}^0$ and $\angle CBD={110}^0$

Answer 1

The correct option is D $\angle CAD={70}^0$ and $\angle CBD={110}^0$

(i) The angle subtended by the diameter at the circumference$={90}^o$.

(ii) The the sum of the opposite angles of a cyclic quadrilateral $={180}^o$.

Hence, $\angle CAD={70}^0$ and $\angle CBD={110}^0$