Math question!!

Test Preparation ACT Preparation
1

<p>Call me stupid, but for some odd reason I cannot figure out question 48 on the student prep packet (the free download off of their website) in the math section. </p>

<ol>
<li>In the circle shown below, chords TR and QS intersect
at P, which is the center of the circle, and the measure
of ∠PST is 30°. What is the degree measure of minor
arc RS ?</li>
</ol>

<p>F. 30°
G. 45°
H. 60°
J. 90°
K. Cannot be determined from the given information</p>

<p>I can't put the picture of the circle in, but it's basically intersected by two lines- QS and TR, and line TS is drawn in. Angle PST is 30 degrees, so how do you figure out what the arc degree measure is?? I guessed F (30) but I guess it's H (60)</p>

<p>I think I'm missing something really obvious... Help me please, you fellow ACT testers!!</p>

2

This is obviously too late for you, but in case other people have problems with it again (it’s in the most recent prep packet again), here’s the solution.

TR and QS pass through the P, the center of the circle. Therefore, TR and QS are diameters. That means that both TP and SP are radii, and therefore equal. In other words, triangle TPS is isosceles with TP and SP being its equal sides. The angles opposite TP and SP must therefore be equal.
Angle T = Angle S = 30.
From this, it follows that angle P = 180-(30+30)=120.
The angle supplementary to 120 is 60, which is your answer.

3

thanks for your help!!