Question

value of x please find​

Answer 1

$\large\underline{\sf{Solution-}}$

In triangle AOB,

$\sf \: \angle \: OAB \: = \: 35 \degree \:$

and

$\sf \: OA = OB \: \: \: \: [ \: radii \: of \: circle \: ]$

$\bf\implies \: \angle \: OAB \: = \: \angle \: OBA$

[ Angle opposite to equal sides are equal ]

$\bf\implies \: \angle \: OAB \: = \: \angle \: OBA \: = \: 35 \degree$

We know, sum of all interior angles of a triangle is supplementary.

So, using this property,

$\sf \: \angle \: OAB \: + \: \angle \: OBA \: + \: \angle \:AOB = \: 180 \degree$

$\sf \: 35 \degree \: + \: 35 \degree \: + \: \angle \:AOB = \: 180 \degree$

$\sf \: 70 \degree \: + \: \angle \:AOB = \: 180 \degree$

$\sf \: \: \angle \:AOB = \: 180 \degree - 70 \degree$

$\bf\implies \: \: \angle \:AOB = \: 110 \degree$

Now,

$\sf \:reflex \angle \:AOB = \:360 \degree \: - \:\angle \:AOB$

$\sf \:reflex \angle \:AOB = \:360 \degree \: - \:110 \degree$

$\bf\implies \:\:reflex \angle \:AOB = \:250 \degree$

We know,

Angle subtended at the centre of a circle by an arc is double the angle subtended on the circumference of a circle by the same arc.

So, using this property, we get

$\sf \:\:reflex \angle \:AOB = 2\angle \:ACB$

$\sf \: 2x = 250 \degree$

$\bf\implies \:x \: = \: 125 \degree$

$\rule{190pt}{2pt}$

Additional Information :-

1. Angle in same segment are equal.

2. Angle in semi-circle is 90°.

3. Equal chords subtends equal angles at the centre.

4. Equal chords are equidistant from center.