SOLUTION: Hello, my name is gabrielle and i been stuck on these four ptoblems for a long time and i was wondering if you could show me the work and the answers? 1.an angle measure 14 deg

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Hello, my name is gabrielle and i been stuck on these four ptoblems for a long time and i was wondering if you could show me the work and the answers? 1.an angle measure 14 deg      Log On

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Question 148907: Hello,
my name is gabrielle and i been stuck on these four ptoblems for a long time and i was wondering if you could show me the work and the answers?
1.an angle measure 14 degress less than three times its compliment. find the measure of the angle and it compliment.

2. the length of a rectangle is 4ft longer than twice its wifth. find the dumension of a rectangle if its perimeter is 58 ft.

2. one angle of a triangle measure 9 degress more than the second angle. the third angle is seven times larger than the second angle. find the measures of each angle of the triangle.
4. the width of a rectangle is 3 feet shorter than its length. the perimeter is 76 decreased by the width. find the dimensions of the rectangle.
i would like for these answer to be answered on july 20th no later than 8 pm. thank yo and have a nice day.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1.an angle measure 14 degress less than three times its compliment. find the measure of the angle and it compliment.
Let the angle be "x"; then the complement is (90-x).
EQUATION:
x = 3(90-x)-14
x = 270-3x-14
4x = 256
x = 64
90-x = 26
------------------------
2. the length of a rectangle is 4ft longer than twice its width. find the dumension of a rectangle if its perimeter is 58 ft.
l = 2w + 4
2l + 2w = 58
-----------------
Rearrange:
l - 2w = 4
l + w = 29
--------------
Subtract the 1st equation from the 2nd to get:
3w = 25
w = 25/3 ft(width)
---------------
Substitute to find "l":
l + (25/3) = 29
l = (87/3)-(25(3)
l = 62/3 ft (length)
================
2. one angle of a triangle measure 9 degress more than the second angle. the third angle is seven times larger than the second angle. find the measures of each angle of the triangle.
1st angle = x degrees
2nd angle = x-9 degrees
3rd angle = 7(x-9) = 7x-63 degrees
-------------
EQUATION:
x + x-9 + 7x-63 = 180
9x -72 = 180
x - 8 = 20
x = 28 degrees (1st angle)
x-9 = 19 degrees (2nd angle)
7(x-9) = 133 degrees (3rd angle)
=============================

4. the width of a rectangle is 3 feet shorter than its length. the perimeter is 76 decreased by the width. find the dimensions of the rectangle.
w = l -3
2l + 2w = 76 - w
---------------------
Rearrange:
2l - 2w = 63
2l+3w = 76
-----------------
Subtract 1st from 2nd to solve for "w":
5w = 13
w = 13/5 ft (width)
-------------
Substitute into l - w = 3 to solve for "l":
l - (13/5) = (15/5)
l = 28/5 ft (length)
========================
Cheers,
Stan H