anonymous
  • anonymous
In a quadrilateral ABCD, the measure of angle A is 2x, the measure of angle B is 3x-15(degrees), the measure of C is 4x-90(degrees), and the measure of angle D is x+15(degrees). Find the value of X, Is ABCD a rectangle? What is the average of the four angles?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
what do you know about the sum of internal angles of a quadrilateral?
anonymous
  • anonymous
x=45(degrees) no abcd is not a rectangle average of angles is=90
anonymous
  • anonymous
not much the whole thing equals 360 degrees

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anonymous
  • anonymous
right, so the sum equals 360. angles A,B,C,D are given. add up all the angles and equate them to 360 post your equation here.
anonymous
  • anonymous
hint: A, B, C, D being angles, A+B+C+D = 360
anonymous
  • anonymous
(2x+3x-15+4x-90+x+15=360) = (10x-90=360) x=45.
anonymous
  • anonymous
right. x = 45. What is the requirement of a quadrilateral to be a rectangle?
anonymous
  • anonymous
ok, so I was doing something like 2x=360 and then trying to solve from there. totally wrong. all quadrilaterals can be solved like this?
anonymous
  • anonymous
all the angle measurements have to be 90 degrees right
anonymous
  • anonymous
yes. so what is the measure of angle A, angle B , angle C and angle D?
anonymous
  • anonymous
a= 90 b=120 c=90 d=60 average=90 =]
anonymous
  • anonymous
why do you care about the average?
anonymous
  • anonymous
ah, okay its asked in the problem. average of the angles of a quadrilateral is always 90, no matter what the angles are.
anonymous
  • anonymous
because a quadrilateral has 4 internal angles and they add up to 360 degrees. so you always end up with 360/4 as the average angle.
anonymous
  • anonymous
okay so what is your conclusion? Is this a rectangle or not?
anonymous
  • anonymous
not a rectangle
anonymous
  • anonymous
WHAT IS THE DISCUSSION TOPIC?
anonymous
  • anonymous
very good.
anonymous
  • anonymous
cool. thanks everybody!
anonymous
  • anonymous
np
yuki
  • yuki
woo

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