Question

In the circle below, QS is a diameter. Suppose m QR = 68° and m<QRT= 56°. Find the following.

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Answer 1

`\boxed{\angle RQS = 56 \ degrees}`

`\boxed{\angle SRT = 56 \ degrees}`

Explanation:

A) ∠QRS = 90 degrees (The angle of the triangle opposite to the diameter is always 90)

Given that QR = 68 degrees

So,

∠RSQ =
`(1)/(2) (QR)`

∠RSQ = 68/2

∠RSQ = 34 degrees

Now, Finding ∠RQS

∠RQS = 180-90-34

∠RQS = 56 degrees

B) ∠SRT = ∠QRS - ∠QRT

=> ∠QRS = 90 (Mentioned above) , ∠QRT = 56 (Given)

So,

∠SRT = 90-56

∠SRT = 34 degrees