Question

In the adjoining figure, if $\angle \text{ABC}={\text{a}}^{\circ }$ and $\angle \text{ADC}={\text{b}}^{\circ }$, then $\text{a}=$

• A. $\text{b}$
• B. $\text{2b}$
• C. $\text{3b}$
• D. $\text{4b}$

Answer 1

The correct option is A $\text{b}$

Given that,
$\angle \text{ABC}={\text{a}}^{\circ }$
$\angle \text{ADC}={\text{b}}^{\circ }$
The above angles are made by the arc $\text{AC}$ at the points $\text{B}$ and $\text{D}$ on the remaining part of the circle.
Note: The measure of all angles subtended by an arc in the same segment of a circle are equal.
So, ${\text{a}}^{\circ }$ and ${\text{b}}^{\circ }$ are same.
$\Rightarrow \text{a}=\text{b}$