△QRS is inscribed in circle P. The measure of a central angle is twice the measure of an inscribed angle that subtends the same arc.

If m ∠QRS = 48°, find m ∠PSQ.
The angles starting at 2 oclock are Q R S

A. 96

B. 84

C. 42

d. 48

Given:

△QRS is inscribed in circle P.

The measure of angle QRS is 48°

We need to determine the measure of angle PSQ.

Measure of ∠PSQ:

It is given that the measure of a central angle is twice the measure of an inscribed angle that subtends the same arc.

Using the above property, we have;

Substituting the values, we have;

Multiplying the values, we get;

Thus, the measure of ∠PSQ is 96°

Hence, Option A is the correct answer.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.