Line P R and Line Q S are diameters of circle T. What is the measure of Arc S R?

50°
80°
100°
120°

Option C:

m(arc SR) = 100°

Solution:

∠PQT = 40°

QT and PT are radii of circle.

QT = PT

ΔPQT is an isosceles triangle.

⇒ ∠PQT = ∠QPT = 40° – – – (1)

Similarly, ΔRST is an isosceles triangle.

⇒ RST = ∠SRT – – – (2)

In ΔPQT and ΔRST,

PT ≅ TR (Radii of circle)

ST ≅ TQ (Radii of circle)

∠PQT ≅ ∠STR (by vertical theorem)

Hence ΔPQT ≅ ΔRST by SAS congruence theorem.

By corresponding parts of congruence triangles are congruent.

∠PQT = ∠RST = 40° (by (1))

∠QPT = ∠SRT = 40° (by (2))

In ΔSTR, sum of all the angles = 180°

40° + 40° + m∠PTQ = 180°

m∠STR = 180° – 80°

m∠STR = 100°

The measure of a central angle and the arc it intercepts are equal in measure.

m∠STR = m(arc SR)

m(arc SR) = 100°

Hence option C is the correct answer.

the answer is y = 11.54

hope this : )

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the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights