A track of land has the shape of a trapezoid the lengths of three sides and two interior right angles are given. Determine the two unknown interior angles and the length of the fourth side.

∠C = 106.7°, ∠D = 73.3°, CD = 104.4

Step-by-step explanation:

As shown in the diagram attached, let a point E be made on line BD.

Hence, BE = 130 m

BE + ED = BD

ED = BD - BE

ED = 160 m - 130 m = 30 m

Also, CE = 100 m

Using Pythagoras theorem in triangle CDE:

CD² = CE² + ED²

CD² = 100² + 30²

CD² = 10000 + 900 = 10900

CD = √10900

CD = 104.4

Using sine rule in triangle CDE:

In trapezoid ABCD, the sum of angles in a quadralateral is 360°, hence:

∠A + ∠B + ∠C + ∠D = 360

90 + 90 + ∠C + 73.3 = 360

∠C + 253.3 = 360

∠C = 360 - 253.3

∠C = 106.7

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed