Help with 3 Geometry Questions

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January 25th 2010, 04:37 PM
LittleLotte

Help with 3 Geometry Questions

Hello everyone!
I've spent hours trying to figure out these last few Geometry questions and I can't seem to find any information on it in my text book. If anyone could offer some help I would really appreciate it. Thank you so much!

1. In the diagram below, ABCD is a parallelogram. What is Angle BEC?
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2. What is the value of x in the diagram below?
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3. What are the values of n and t in the kite below?
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a. n= 4 t= 39
b. n= 4 t= 51
c. n= 4.5 t= 39
d. n=4.5 t= 51
January 25th 2010, 05:22 PM
LittleLotte

I only have until 9 tonight to finish these questions so I REALLY would appreciate the help. I've tried every resource I could. Please help.
January 25th 2010, 07:19 PM
Soroban

Hello, LittleLotte!

Quote:

1. In the diagram below, $ABCD$ is a parallelogram.
What is angle $BEC$ ?

Code:

A o * * * * * o B * * 30° * * * * * * * o E * * * * * * * 35° * * D o * * * * * o C

We are given: . $\angle BAE = 30^o$

Since $AB \parallel DC$ . then: $\angle ECD = \angle BAE$ .(alterate-interior angles)

Then $\angle ECD = 30^o$

In $\Delta EDC$ , we know two angles: . $\angle EDC = 35^o,\;\angle ECD = 30^o$

Hence, the third angle is: . $\angle DEC \:=\:180^o - 35^o - 30^o \:=\:115^o$

$\angle BEC$ and $\angle DEC$ are supplementary: . $\angle BEC + \angle DEC \:=\:180^o$

So we have: . $\angle BEC + 115^o \:=\:180^o \quad\Rightarrow\quad\boxed{ \angle BEC \,=\,65^o}$
January 25th 2010, 10:16 PM
Archie Meade

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Quote:

Originally Posted by LittleLotte

2. What is the value of x in the diagram below?
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The upper and lower triangles are identical, due to opposite corner angles being equal, touching angles equal and parallel sides equal length.

Hence 2a+2=4 so 2a=4-2=2, a=1

x=a+3.5=1+3.5=4.5
January 25th 2010, 10:23 PM
Archie Meade

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Quote:

Originally Posted by LittleLotte

3. What are the values of n and t in the kite below?
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a. n= 4 t= 39
b. n= 4 t= 51
c. n= 4.5 t= 39
d. n=4.5 t= 51

All 3 angles in a triangle sum to 180 degrees.
In a right-angled triangle, one angle is 90 degrees.
180-90=90 so t and 51 degrees sum to 90 degrees, so t=90-51=39 degrees.

If the side of length 2n equals the side below it, then the side 3n-4 equals the side n+5 in length.

n+5=3n-4, n+5+4=3n, n+9=3n, n-n+9=3n-n=2n, 9=2n, n=9/2=4.5