Question

the diameter of circle with centre O and AT is a tangent if anle AOQ=58°,find anle ATQ

Answer 1

the measuŗment of angleATQ is 32 degre

Answer 2

Answer:

∠ATQ = 61°

Step-by-step explanation:

For better understanding of the solution, see the attached figure :

Given : ∠AOQ = 58° . AB is diameter of circle.

To find : ∠ATQ

Solution : Since the angle formed at the center is twice the angle formed by the same chord at any other point on the circle.

⇒ ∠AOQ = 2∠ABQ

⇒ 58° = 2∠ABQ

⇒ ∠ABQ = 29°

Also, Tangent makes right angle with the radius of the circle

⇒ ∠BAT = 90°

Now, using angles sum property of a triangle in ΔBAT

⇒ ∠BAT + ∠ABT + ∠ATB = 180°

⇒ 90 + 29 + ∠ATB = 180

⇒ ∠ATB = 180 - 119

⇒ ∠ATB = 61°

So, ∠ATQ = 61°