Question

An architect designs two similar triangular patios. The first patio has angle measures of (x + 10)°, (y + 5)°, and 40°. The second patio has angle measures of (x – 10)°, 60°, and 80°. Find the values of x and y.
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Answers

  1. Answer: x = 50, y = 75
    The sum of angles of a triangle is equal to 180°
    according to the question, (x+10) + (y+5) + 40 = 180 — eq(1)
    (x-10) + 60 + 80 = 180 — eq(2)
    (x – 10) + 140 = 180
    x – 10 +140 = 180
    x + 130 = 180 , x = 180 – 130
    x = 50
    put x value in eq(1)
    50+10 + (y+5) + 40 = 180
    60+(y+5)+40 = 180
    y+5 +100 = 180
    y + 105 = 180
    y = 180 – 105
    y = 75
    So, x = 50 and y = 75.
    To learn more about triangles,

  2. Answer: x=230 and y=75
    Step-by-step explanation: A triangle is worth 360 degrees, which means when you add up all the angles it equals 360 degrees. So
    Second patio:
    (x-10),60+80 = 360
    x-10+140 =360-140
    x-10=220+10
    x=230
    First patio:
    (x+10)+(y+5)+40 = 360
    x+y+55=360
    x+y=360-55
    x+y=305- x(230) =75
    y=75

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