Math, asked by parulagarwalclass10b, 5 months ago

AB is a diameter of a circle with centre O and AT is a tangent if angle AOQ is equal to 58 degree find angle ATQ​

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Answers

Answered by nittuamu
4

Answer:

angle ATQ= 61 degree

Step-by-step explanation:

We know that the angle subtended by an arc of a circle at the center is twice the angle suntended by it at any point on the remaining part of the circle.

angle AOQ=2angleABQ

angleABQ=1/2angleAOQ

angleABQ=1/2*58degree

angleABQ=29degree

or

angle ABT=29degree

We know that the radius is perpendicular to the tangent at the point of contact.

angle OAT=90degree(OA is perpendicular to AT)

or

angleBAT=90degree

Now in BAT

angleBAT+angleABT+angleATB=180degree

90degree+29degree+angleATB=180degree

119degree +angleATB=180degree

angleATB=180degree-119degree

angleATB=61degree

therefore, angleATQ=61degree

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