In circle T, what is the value of x?
2 answers:
Answer:
x = 19°
Step-by-step 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 .
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