Question

If m ST = 96°, then m∠Q=m∠R.
True
False

Answer 1

Option A. True

Explanation:

As we know Inscribed angle theorem states that measure of an inscribed angle is equal to half of the measure of its intercepted arc.

Since m ST = 96°

Therefore ∠ TQS = 96/2 = 48°

Similarly ∠ TRS = 96/2 = 48°

Which clearly states that ∠TQS = ∠TRS = 48°

Or m∠Q = m∠R = 48°

Therefore option A. True is the correct option.

Answer 2

True

Explanation:

we know that

The inscribed angle is half that of the arc it comprises.

so

In this problem

`m<Q=(1)/(2)(arc\ ST)`

substitute the value

`m<Q=(1)/(2)(96\°)=48\°`

`m<R=(1)/(2)(arc\ ST)`

substitute the value

`m<R=(1)/(2)(96\°)=48\°`

therefore

`m<Q=m<R=48\°`