Question

HELP ME PLEASE !!!

Given that ∠BDC = 29° ∠BCA = ____ ° AND ∠BOC = ____ °

19.5
29
58

Answer 1

Instead of ∠BCA it should be ∠BAC and the value of this will be 29.
The value of ∠BOC is 58 ...this is the property of circle ...29 +29=58

Answer 2

`\angle BAC=29^(\circ)`

`\angle BOC=58^(\circ)`

Explanation:

We have been given a circle in which measure of ∠BDC is 29°.

We can see that angle BDC and angle BAC are inscribed angles of arc BC. Since both angles corresponds o same arc, therefore, measure of angle BAC would be 29 degrees.

We can see that angle BOC is central angle and measure of central angle is twice the measure of inscribed angle, when both corresponds to same arc.

`\angle BOC=2* \angle BAC`

`\angle BOC=2* 29^(\circ)`

`\angle BOC=2* 58^(\circ)`

Therefore, measure of angle BOC would be 58 degrees.