The area of the rectangle is A. 6000
X = 5/3 and m∠SPY = 8 1/3°.
Since PQ bisects the angle, the two angles formed by the bisector are equal:
11/2x - 5 = 4x - 5/2
We will first multiply everything by 2 to eliminate the fractions:
(11/2x)*2 - 5*2 = 4x*2 - (5/2)*2
11x - 10 = 8x - 5
Subtract 8x from each side:
11x - 10 - 8x = 8x - 5 - 8x
3x - 10 = -5
Add 10 to both sides:
3x - 10 + 10 = -5 + 10
3x = 5
Divide both sides by 3:
3x/3 = 5/3
x = 5/3
Now we will plug this in for x in both smaller angles and add them together to find the measure of ∠SPY:
11/2(5/3) - 5 + 4(5/3) - 5/2
55/6 - 5 + 20/3 - 5/2
We will rewrite everything using a denominator of 6:
55/6 - 30/6 + 40/6 - 15/6 = (55-30+40-15)/6 = 50/6 = 8 2/6 = 8 1/3°
When naming triangles we name them by the letters on each corner so only answers with T, A, and X in them are correct, so TAX, XTA, and AXT
So the two numbers can be represented as x and y
so x is first and y is second
y=2(x)-8
so y=2x-8
IF THEY ARE CONSECUTIVE
If they are consecutive numbers then
x+1=y
subtitute
x+1=2x-8
subtract x from both sides
1=x-8
add 8 to both sides and get
9=x
put it into the equation and get
y=2(9)-8
y=18-8
y=10
so x=9
y=10
IF X AND Y ARE CONSECUTIVE INTEGERS (1,2,3,4 not 2.3 or 1,3,5,8)
