Answer:
YU = 4.82. angle STR = 23°
Explanation:
7) Angle between U and V = 72°, since angles on a straight line add up to 180°. so angle UV = 180 - 108 = 72°.
similarly, angle YU = 180 - 85 - 72 = 23°.
length of circumference of full circle = π X diameter = π (2r)
= 2πr (radius = half of diameter).
circumference = 2π(12) = 24π.
there are 360° in full circle.
remember that angle YU = 23°.
length YU = (23/360) X 24π
= (23π)/15
= 4.817
= 4.82 to nearest one hundredth.
8) triangle RST sits inside of half the circle, ie in the semicircle.
angle RST = 90° because the angle in a semicircle = 90°.
there are 180° in a full triangle.
since angle RST = 90°, angle STR must be less than 180 - 90.
angle STR < 90°. so STR must be 23°.