Answer:
Arc DE = 70°
Arc RST = 206°
Step-by-step explanation:
arc DE + arc DC = 180° because EC is a diameter
7x + 7 + 11x + 11 = 180°
combine like terms:
18x + 18 = 180°
subtract 18 from both sides of the equation:
18x = 162°
divide both sides by 18:
x = 9
Arc DE = 7(9) + 7 = 70°
arc RST = 2(x + 103) = 2x + 206
arc RFT = 2(x + 77) = 2x + 154
arc RST + arc RFT = 360°
so:
2x + 206 + 2x + 154 = 360°
combine like terms:
4x + 360 = 360
4x = 0
x = 0
arc RST = 2x + 206 = 206°
