# Thread: Help with 3 Geometry Questions

1. ## 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

2. 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.

3. Hello, LittleLotte!

1. In the diagram below, $\displaystyle ABCD$ is a parallelogram.
What is angle $\displaystyle BEC$?
Code:
    A o  *  *  *  *  *  o B
*  * 30°       *  *
*     *     *     *
*        o E      *
*     *     *     *
*  * 35°       *  *
D o  *  *  *  *  *  o C

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

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

Then $\displaystyle \angle ECD = 30^o$

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

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

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

So we have: .$\displaystyle \angle BEC + 115^o \:=\:180^o \quad\Rightarrow\quad\boxed{ \angle BEC \,=\,65^o}$

4. 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

5. 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