Answer:
- Arc QR = 48°; Arc RS = 96°
- x = 74/7; y = 15
Step-by-step explanation:
Given two inscribed quadrilaterals with various arcs and angles marked, you want to solve for specific unknown values.
1.
The measure of an inscribed angle is half the measure of the arc it intercepts. The sum of arcs of a circle is 360°.
Arc PSR = 2·∠PQR = 2·93° = 186°
Arc RS = Arc PSR -Arc PS = 186° -90° = 96°
Arc QR = 360° -126° -90° -96° = 48°
The unknown arcs are ...
2.
Opposite angles in an inscribed quadrilateral are supplementary:
105° +(7x +1)° = 180°
7x = 74 . . . . . . . . . . . divide by °, subtract 106
x = 74/7 = 10 4/7 . . . . . divide by 7
(4y +14)° +(7y +1)° = 180°
11y = 165 . . . . . . . divide by °, subtract 15
y = 15 . . . . . . . . . divide by 11
The values of x and y are ...
