Question

Communication

ABC and DEF are straight lines.
AC is parallel to DF.
BE = CE
Work out the value of x.
Give reasons for your answer.
A
D
132°
B
E
12
x
C
LL
F

Answer 1

To find the value of x in this geometry problem, we can use the properties of parallel lines and corresponding angles.

Given:

ABC and DEF are straight lines (which means they are 180 degrees each).
AC is parallel to DF.
BE = CE.
We need to determine the value of x.

First, let's focus on the angles formed by these lines:

Angle ADC (the angle at point D) is 132°.
Angle EBC (the angle at point B) and Angle ECD (the angle at point C) are equal because BE = CE.
Now, let's use the fact that AC is parallel to DF:

Angle ADC (132°) and Angle ECD (the angle at point C) are corresponding angles, which means they are equal.
So, we have:
Angle ECD = 132°

Now, we know that the sum of angles around point C should be 360 degrees:

Angle EBC + Angle ECD + x = 360°

We already know that Angle ECD is 132°, and since BE = CE, Angle EBC must be equal:

Angle EBC = Angle ECD = 132°

Now, let's substitute these values into the equation:

132° + 132° + x = 360°

Combine like terms:

264° + x = 360°

Now, isolate x:

x = 360° - 264°

x = 96°

So, the value of x is 96 degrees.