Question
A quadrilateral is inscribed in a circle. Two consecutive angles measure 88 degrees and 108 degrees. The angle opposite the 108 degrees is labeled x. find the value of x
Answers
GPT-4o mini
In a cyclic quadrilateral (a quadrilateral inscribed in a circle), the opposite angles are supplementary. This means that the sum of the measures of opposite angles equals \(180^\circ\).
Given the angles of the quadrilateral:
- One angle measures \(88^\circ\)
- The consecutive angle measures \(108^\circ\)
- The angle opposite the \(108^\circ\) angle is labeled \(x\)
Since the opposite angles \(108^\circ\) and \(x\) are supplementary, we have:
\[
108^\circ + x = 180^\circ
\]
Now, we can solve for \(x\):
\[
x = 180^\circ - 108^\circ = 72^\circ
\]
Therefore, the value of \(x\) is \(72^\circ\).
Given the angles of the quadrilateral:
- One angle measures \(88^\circ\)
- The consecutive angle measures \(108^\circ\)
- The angle opposite the \(108^\circ\) angle is labeled \(x\)
Since the opposite angles \(108^\circ\) and \(x\) are supplementary, we have:
\[
108^\circ + x = 180^\circ
\]
Now, we can solve for \(x\):
\[
x = 180^\circ - 108^\circ = 72^\circ
\]
Therefore, the value of \(x\) is \(72^\circ\).