Question

Which of the following option is correct?

• A. $a=2s,b=2t$
• B. $a=2t,b=2s$
• C. $t=2a,s=2b$
• D. $t=2b,s=2a$

Answer 1

The correct option is A $a=2s,b=2t$

For the given $△\text{ACD}$
$\angle \text{CDA}=t$
$\angle \text{ACD}=t$
And $\angle \text{CAB}=b$, (exterior angle)
Note: Exterior angle is equal to the sum of opposite angles.
$\therefore \angle \text{CAB}=\angle \text{CDA}+\angle \text{ACD}$
$b=t+t$
$\Rightarrow b=2t$

For the given $△\text{ABC}$
$\angle \text{BCA}=s$
$\angle \text{ABC}=s$
And $\angle \text{CAD}=a$, (exterior angle)
$\therefore \angle \text{CAD}=\angle \text{BCA}+\angle \text{ABC}$
$a=s+s$
$\Rightarrow a=2s$