Question

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?

Answer 1

what do you know about the sum of internal angles of a quadrilateral?

Answer 2

x=45(degrees) no abcd is not a rectangle
average of angles is=90

Answer 3

not much the whole thing equals 360 degrees

Answer 4

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.

Answer 5

hint:

A, B, C, D being angles,
A+B+C+D = 360

Answer 6

(2x+3x-15+4x-90+x+15=360) = (10x-90=360) x=45.

Answer 7

right. x = 45.
What is the requirement of a quadrilateral to be a rectangle?

Answer 8

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?

Answer 9

all the angle measurements have to be 90 degrees right

Answer 10

yes.
so what is the measure of angle A, angle B , angle C and angle D?

Answer 11

a= 90 b=120 c=90 d=60 average=90 =]

Answer 12

why do you care about the average?

Answer 13

ah, okay its asked in the problem. average of the angles of a quadrilateral is always 90, no matter what the angles are.

Answer 14

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.

Answer 15

okay so what is your conclusion? Is this a rectangle or not?

Answer 16

not a rectangle

Answer 17

WHAT IS THE DISCUSSION TOPIC?

Answer 18

very good.

Answer 19

cool. thanks everybody!

Answer 20

np

Answer 21

woo