YOU have a circle with a traingle inside. P being the top of triangle and Q and R, are on the sides, PQ= (8x-10) and PR=(6x) and the bottom QR= (10x+10)

SAYS:
a)find X
b)is the triangle equilateral, isosceles, or scalene?
explain.

We have not done this type of work, this is all the teacher gave for help below.
a)It says to find x you will need to add the arc measures together and set this expression equal to the total degrees of a circle and then solve for x.
b)Here are the steps
1) plug your x-value from a into each of the arc measures to find what each arc measures.
2) apply the inscribed theorem to find <P, <R, and <S
3) use the angle measure from step 2 above to determine what type oftriangle you have.

The answer is
a=15
b=scalene, the arc measures are 110, 90, 160, the arcs are not congruent neither are the chords that intercept.
Hope this helps and someone can explain the steps to me as I'm confused.

At first, I was having difficulty understanding the given. I thought the PQ, PR and QR are the lengths of the triangle, but they are actually the arc (angle measure).

Anyway, to get x, we know that the measure of a circle is 360 degrees. We get the sum of arcs PQ, PR and QR and equate it to 360:
(8x - 10) + 6x + (10x + 10) = 360
24x = 360
x = 15
now we substitute this back to the measure of the arcs:
PQ = 8*15 - 10 = 110 degrees
PR = 6*15 = 90 degrees
QR = 10*15 + 10 = 160 degrees

Then, recall inscribed angle theorem. The measure of an inscribed angle (in this case, an interior angle of the triangle) is half the measure of the arc it subtends. Thus the interior angles of the triangles are half of PQ, PR and QR, which are 55, 45 and 80.
The triangle is SCALENE because there are no angles of equal measure.

hope this helps~ :)

To find X in this problem, you need to use some geometry concepts and equations.

a) To find X, you need to add the arc measures together and set them equal to the total degrees of a circle, which is 360 degrees. Let's first find the measures of the arcs PQ, PR, and QR.

PQ = (8x - 10)
PR = (6x)
QR = (10x + 10)

Add the three arc measures together:
PQ + PR + QR = (8x - 10) + (6x) + (10x + 10)

Simplify the equation:
8x - 10 + 6x + 10x + 10 = 360

Combine like terms:
24x = 360

Divide both sides by 24:
x = 15

So X equals 15.

b) To determine the type of triangle (equilateral, isosceles, or scalene), we need to follow the given steps:

1) Plug the value of x (which we found as 15) into each of the arc measures to find what each arc measures.

PQ = (8x - 10) = (8 * 15 - 10) = 110
PR = (6x) = (6 * 15) = 90
QR = (10x + 10) = (10 * 15 + 10) = 160

2) Apply the inscribed angle theorem to find the measures of angles P, Q, and R. The inscribed angle theorem states that an angle formed with endpoints on a circle is half the measure of the intercepted arc.

Angle P = PQ/2 = 110/2 = 55 degrees
Angle Q = PR/2 = 90/2 = 45 degrees
Angle R = QR/2 = 160/2 = 80 degrees

3) Use the angle measures from step 2 to determine the type of triangle.

In an equilateral triangle, all angles are congruent. Since angles P, Q, and R have different measures, the triangle is not equilateral.

In an isosceles triangle, two angles are congruent. Since angles Q and R have different measures, the triangle is not isosceles.

In a scalene triangle, all angles have different measures. Since angles P, Q, and R have different measures, the triangle is scalene.

Therefore, the triangle is scalene because the arc measures are 110, 90, and 160, and the arcs and chords that intercept are not congruent.