This figure is an inscribed quadrilateral because it is a 4-sided figure and its vertices all lie on a circle. This means that the two pairs of opposite angles each add up to 180°. Make them add up to 180 in 2 separate equations, to find x and to find y.
105 + (7x + 1) = 180
(4y + 14) + (7y +1) = 180
Solve the first equation first. Combine like terms (105 + 1).
106 + 7x = 180
Subtract 106 from both sides.
7x = 74
Divide both sides by 7.
x = 10.6 (rounded to tenths place) or [tex] \frac{74}{7} [/tex].
Solve the second equation. Combine like terms (4y + 7y), (14 + 1).
11y + 15 = 180
Subtract 15 from both sides.
11y = 165
Divide both sides by 11.
y = 15
x= 10.6, y = 15
