Question

Solve angle x. Fastttttt

Plz dont type something that is unreleated.

Answer 1

$\Huge{\boxed{\red{\mathbb{QUESTION}}}}$

To find the value of x.

$\Huge{\boxed{\blue{\mathbb{ANSWER}}}}$

As in the figure,

We have to find the value of ∠AOB which is represented as x.

In △CAT,

∠TCA = 48°

∠CTA = 36°

But,

∠CTA + ∠TCA + ∠CAT = 180° [Angle sum property of a triangle].

36° + 48° + ∠CAT = 180°

84° + ∠CAT = 180°

∠CAT = 180° - 84°

∠CAT = 96°

Also,

∠CAT + ∠CAB = 180° [linear pairs]

96° + ∠CAB = 180°

∠CAB = 180° - 96°

∠CAB = 84°

As OA is angle bisector of ∠A,

∠OAB = $\frac{1}{2} ∠CAB$

∠OAB = $\frac{1}{2} 84°$

∠OAB = 42°

Let ∠OAB represent as y.

Then, ∠OBA = y [∠OBA and ∠OAB meet at the centre of the circle.]

In △OAB,

∠OBA + ∠OAB + ∠AOB = 180° [Angle sum property of a triangle].

y+y+x = 180°

42° + 42° + x = 180°

84° + x = 180°

x = 180° - 84°

x = 96°

$\large{\bold{\underline{Therefore,\:∠AOB\:=\:96°.}}}$