Question
A circumcenter has P at the top and to the right of it,it has (8x-10) degrees and to the right it has (6x) degrees and the right hand bottom it’s Q and to the left hand bottom it’s R at the bottom of the circle it’s (10x+10) degrees. Find X
Answers
Answered by
GPT-4o mini
To find the value of \( x \) based on the angles given at the circumcenter, we first note that the angles around a point add up to \( 360^\circ \).
You described the angles at the circumcenter as follows:
1. \( \angle P = (8x - 10)^\circ \)
2. \( \angle Q = (6x)^\circ \)
3. \( \angle R = (10x + 10)^\circ \)
The sum of these angles must equal \( 360^\circ \):
\[
(8x - 10) + (6x) + (10x + 10) = 360
\]
Now we combine the like terms:
\[
8x - 10 + 6x + 10 + 10x = 360
\]
Simplifying this gives:
\[
(8x + 6x + 10x) + (-10 + 10) = 360
\]
\[
24x = 360
\]
Next, we solve for \( x \):
\[
x = \frac{360}{24} = 15
\]
Thus, the value of \( x \) is \( \boxed{15} \).
You described the angles at the circumcenter as follows:
1. \( \angle P = (8x - 10)^\circ \)
2. \( \angle Q = (6x)^\circ \)
3. \( \angle R = (10x + 10)^\circ \)
The sum of these angles must equal \( 360^\circ \):
\[
(8x - 10) + (6x) + (10x + 10) = 360
\]
Now we combine the like terms:
\[
8x - 10 + 6x + 10 + 10x = 360
\]
Simplifying this gives:
\[
(8x + 6x + 10x) + (-10 + 10) = 360
\]
\[
24x = 360
\]
Next, we solve for \( x \):
\[
x = \frac{360}{24} = 15
\]
Thus, the value of \( x \) is \( \boxed{15} \).