Question

please answer this question fast . ​

Answer 1

Given :-

• ∠ACB = 40°
• OA = OB = x .........(∵Radius of the circle )

To find :-

• ∠OAB = x = ?

Therefore, by theorem,

• The angle subtended by an arc at the centre is twice the angle subtended by the same arc at some other point on the remaining part of the circle.

$\\ \mathtt{ \leadsto\ ∠AOB = 2 \times ACB}$

$\\ \mathtt{ \leadsto\ ∠AOB = 2 \times 40 \degree}$

$\\ \color{green} \mathtt{ \leadsto\ ∠AOB =80 \degree}$

Therefore, By angle sum property of triangle,

$\mathtt{\implies ∠AOB + ∠OAB + ∠OBA = 180°}$

$\mathtt{\implies80 \degree +x + x= 180°}$

$\mathtt{\implies80 \degree + 2x = 180 }$

$\mathtt{\implies2x = 180 - 80}$

$\mathtt{\implies2x = 100}$

$\\ \mathtt{\implies \: x = \frac{100}{2} }$

$\color{green}{ \LARGE{ \mathtt{\implies \: x = 50 \degree}}}$

Therefore, value of x is 50°