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.

We first calculate  Pablo's height .

4 = 100%

x = 1%  (Where x is 1% of  Sandra's height.)

cross multiplying the equation, we get:

100x = 4 →  x = 4/100  → x = 0.04

If 1% = 0.04, then 10%  will be 0.04 × 10 = 0.4

Pablo's height is 4 + 0.4 =  4.4 feet.

Now we repeat the above steps to get Michal's height from Pablo's height

4.4 = 100%

x =  1%       so:

100x = 4.4 → x = 4.4/ 100 → x = 0.044

If 1% = 0.044, then 8% will be 0.044 × 8 = 0.35

Michael's height is  4.4 + 0.35 = 4.75 feet.