Quadrilateral STWR is inscribed inside a circle as shown below. Write a proof showing that angles T and R are supplementary. Cir
cle Q is shown with an inscribed quadrilateral labeled RSTW.
1 answer:
Consider the figure attached.
Let m(R)=α degrees and m(T)=β degrees.
1.
Angle R, is an inscribed angle, intercepting the arc WTS.
This means that the measure of the arc WTS is double the measure of the angle R,
so m(arc WTS) = 2α degrees.
2.
Similarly,
Angle T, is an inscribed angle, intercepting the arc WRS. So
m(arc WRS) = 2β degrees.
3.
m(arc WTS)+m(arc WRS)=360° since these arcs cover the whole circle.
thus
2α+2β=360°
divide by 2:
α+β=180°
this means T and R are supplementary angles.
Let m(R)=α degrees and m(T)=β degrees.
1.
Angle R, is an inscribed angle, intercepting the arc WTS.
This means that the measure of the arc WTS is double the measure of the angle R,
so m(arc WTS) = 2α degrees.
2.
Similarly,
Angle T, is an inscribed angle, intercepting the arc WRS. So
m(arc WRS) = 2β degrees.
3.
m(arc WTS)+m(arc WRS)=360° since these arcs cover the whole circle.
thus
2α+2β=360°
divide by 2:
α+β=180°
this means T and R are supplementary angles.
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Answer:
111 points
Step-by-step explanation:
First, thing I like to do is to convert word problems into an eqaution or write down the important information. So, Math = 37 points and now the points are tripled because of where she placed the word. Also, tripled is implying that her base score for the word is 3 times the original value.
So,
= 111 points.