Question

burtin, jacameron
formative: unit 6: g.gsr.8.1 abridged
5 of 5
find the value of each variable.
○ $x = 75^\circ$ and $y = 78^\circ$
○ $x = 78^\circ$ and $y = 65^\circ$
○ $x = 102^\circ$ and $y = 115^\circ$
○ $x = 71.5^\circ$ and $y = 71.5^\circ$

Explanation:

Step1: Use cyclic quadrilateral property

In a cyclic quadrilateral, opposite angles sum to $180^\circ$.

Step2: Solve for $x$

Set up equation for $x$:
$x + 102^\circ = 180^\circ$
$x = 180^\circ - 102^\circ = 78^\circ$

Step3: Solve for $y$

Set up equation for $y$:
$y + 115^\circ = 180^\circ$
$y = 180^\circ - 115^\circ = 65^\circ$

Answer:

x = 78° and y = 65°