How do your solve this inscribed polygon problem?

Question

asked Apr 18, 2024 196k views

1 Answer

Lemieuxster · Answer 1 · 2024-04-23T10:21:06+0000

The sum of the opposite angles in a cyclic quadrilateral is
$180^(\circ)$ .

Therefore

$6y+23+7x-3=180^(\circ)\\8y-5+7x-5=180^(\circ)\\\\6y+7x=160^(\circ)\\8y+7x=190^(\circ)$

Subtracting the second equation from the first one, we get:

$2y=30^(\circ)\\y=15^(\circ)$

$6\cdot15^(\circ)+7x=160^(\circ)\\90^(\circ)+7x=160^(\circ)\\7x=70^(\circ)\\x=10^(\circ)$