AB intersects CD at E. If m<AED is represented by 2x-5 and m<BEC is represented by x+15, find m<BED
To find m<BED, we can use the fact that the angles around a point add up to 360 degrees.
First, let's set up an equation using the given information:
m<AED + m<BEC + m<BED = 360
Substituting the given values:
2x-5 + x+15 + m<BED = 360
Combining like terms:
3x + 10 + m<BED = 360
Now, let's isolate m<BED by subtracting 10 from both sides:
3x + m<BED = 350
Finally, to solve for m<BED, we need to know the value of x. If you have any additional information or a way to find the value of x, we can proceed with solving the equation.
To find the measure of ∠BED, we need to use the properties of intersecting lines.
Since AB intersects CD at point E, we can conclude that ∠AED and ∠BEC are vertical angles. By definition, vertical angles are congruent, which means that they have the same measure.
So, we set up an equation to represent this relationship:
2x - 5 = x + 15
Now, let's solve this equation to find the value of x.
2x - x = 15 + 5
x = 20
Now that we know the value of x, we can substitute it into either one of the angle measures to find the measure of ∠AED.
m<AED = 2x - 5 = 2(20) - 5 = 40 - 5 = 35 degrees
Similarly, we can substitute x into the other angle measure to find the measure of ∠BEC.
m<BEC = x + 15 = 20 + 15 = 35 degrees
Since ∠AED and ∠BEC are vertical angles and have the same measure, we can conclude that both angles measure 35 degrees.
Therefore, the measure of ∠BED is also 35 degrees, as it is an adjacent angle to ∠BEC and shares the same intersection point with AB.
But AED and BEC are opposite angles and equal so
2x-5 = x+15
x = 20
AED + BED = 180
but AED = 2(20) - 5 = 35
so
35 + BED = 180
BED = 145