Question

In circle T, what is the value of x?

x = 19°

x = 20°

x = 24°

x = 29°

Answer 1

x equals 19 hope this helps

Answer 2

x = 19°

Explanation:

Refer the attached figure

Given : ∠ACB = 71°

∠BAC = x°

Thales' theorem : If A, B, and C are distinct points on a circle where the line AC is a diameter, then the angle ∠ABC is a right angle.

So, by Thale's theorem ∠ABC is a right angle in the given figure

i.e.∠ABC = 90°

In ΔABC ,

To find x we will use angle sum property of triangle

Angle sum property of triangle : Sum of all angles is 180°

⇒∠BAC+∠ABC+∠ACB = 180°

⇒x°+90°+71° = 180°

⇒x°+161° = 180°

⇒x° = 180°-161°

⇒x° =19°

∠BAC = x° =19°

Thus x = 19°

Hence Option 1 is correct .