Question

what is the size of the angle CBX​

Answer 1

Step-by-step explanation:

In triangle AOX, angle angle X= 85(V.O.A)

32+85+angle A=180(A.S)

117+angle A=180

angle A=180-117=63

angle CBX = angle B=63(since angle in the same segment are equal)

Answer 2

The size of the angle CBX is 63°.

Given,

Refer figure,

∠ADX = 32°.

∠BXC = 85°.

To find,

∠CBX.

Solution,

Here, it can be seen from fig. that, ∠BXC and ∠AXD are vertically opposite angles.

Since vertically opposite angles are always equal,

∴ ∠BXC = ∠AXD = 85°

⇒ ∠AXD = 85°

As sum of all 3 angles of a triangle is equal to 180°.

In ΔADX,

∠ADX + ∠AXD + ∠DAX = 180

⇒ 32 + 85 + ∠DAX = 180

⇒ ∠DAX = 180 - (32 + 85)

⇒ ∠DAX = 180 - 117

⇒ ∠DAX = 63°

Now, as we know that the angles in the same segment of a circle are equal. Or, an arc subtends equal angles anywhere on the circumference of a circle.

Consider the arc DC here. The angles subtended by this arc are ∠CBX and ∠DAX.

⇒ ∠CBX = ∠DAX

∴ ∠CBX = 63°.

Therefore, the size of the angle CBX​ is 63°.